If you don't like pick noise, change your angle of attack.  Do not hold the pick rigidly vertical like this ...|... Instead, turn your wrist as you strum out and back so that the pick slides across the strings at a flat angle,  like this ///  and this \\\   but even flatter.  Robert Force likens the motion as similar to when you burn your fingers pulling off a toasted marshmallow -- and whip your hand back and forth to cool them off...   Don't strum by rotating the arm at the elbow hold the hand rigidly, but by rotating the hand at the wrist. 

Exploring the world of plectra is almost a hobby all by itself! I love my collection of picks, and I'm sure I am not alone in this. So many different materials, shapes, colors and thicknesses.  I sort them into different little Altoid tins.  There's even a tin in my desk drawer at work to fidget with while I'm on the phone or in a Zoom meeting.  Brings me calm comfort and joy. I have hand-made ones from buttons and coconut shell and coins.  I have an off-brand green cellulose pick that sounds the best on my dulcimer, but awful on my other instruments. I may never get used to thumb picks, but I have a few. Experiment and find the sound you want!

Those are good. But if you want less pick noise, you might try the Dunlop Jazz III. They’re small, so not much point. They’re a thick, mellow pick.

you can decrease the bad noises using a Dunlop nylon pick (they are grey).
They are less noisy than plastic picks (and they never brake !).
I use 0,73 for dulcimer and 0,88 for guitar.

Just my opinion, I personally do not care for pick noise, but that is just me.

Everyone is correct here about the difference in picks, it comes down to the size of the pick, the thickness or thinness, what the pick is made of, and where you strum on the instrument (if you strum in the hollow or more on the fretboard.) It is also how hard or soft you strum and how much pick travels across the strings…do you hold it close to the pick edge or farther back. I guess what I mean is how much of the pick is exposed from where you hold it. Is it a tiny bit or is it like a 1/4th inch. Also do you hold the pick in a horizontal or vertical position. Everyone is individual and that is a good thing.

I have always used a thin metal corset stave to strum with and the metal striking the metal strings makes virtually no pick noise at all. This proves that anyone can find the right sound for them…

Best wishes…

Thank you all for your replies.  For some songs, I agree that the percussive click adds a cool rhythm element, just like it does on guitar.  It made a really big difference when I switched from the thin, large triangular pick that came with the dulcimer to one of my thicker guitar picks, where I don't have as much of the point exposed.  As a new dulcimist, I wouldn't have reached those conclusions on my own this quickly without your help!

Last night, I realized I'd learned all but one chord to James Taylor's cowboy lullabye, "Sweet Baby James," so I looked up Bm and started playing.  Suddenly, it felt like I was back on the steps at my grandparents' home in south Arkansas in 1972, struggling to change through the same chords on my first guitar.  So my new-to-me dulcimer has already brought back some wonderful memories and enabled me to appreciate the joy of learning an old, old favorite--all over again in a new way. 

A few comments, some of which have already been stated.

A thicker pick will lead to less pick clack.

Holding the pick so that less sticks out of your fingers will decrease the contact between the pick and the fretboard. Remember that you only have to graze the top of the strings. You don't have to actually dig down beneath them.

Some pick materials make more clack than others.  I am not  fan of the felt picks Lois recommends because it is too hard to pick individual strings or play fast.  But you might experiment with different brands of picks and different models from different brands and see if some have less clack than others.  (I've actually started using pretty expensive picks because they have a warmer, less plasticky tone and very little pick clack. But the really expensive one I have was given as a gift. I would never spend $35 on a single pick, and you shouldn't either!)

You probably hear the pick clack more than your audience.

Some people, as Strumelia explains, don't mind the pick clack at all.  Personally, I enjoy hearing fingers sliding on strings and picks hitting the instrument. It's a reminder that playing an instrument is a tactile experience as well as a musical one and is not merely a computer producing clean digital tones. (I like to hear the valve noise of jazz saxophone players, too.)

If you really hate it, play with your fingers.  I love the soft sound of bare fingertips caressing the strings.  Linda Brockinton and Nina Zanetti play such moving music. You can, too.

This won't help with any "bad habit", but if you're playing a piece where you don't want that percussive sound I strongly recommend felt picks.  I also find they don't produce as loud a sound.  I tend to think of myself as having a fairly strong voice, but picks produce so much louder sounds that it can be hard to be heard over it in an acoustic setting without a microphone.

Pick click comes from a couple of things.  Thinness of the pick; how deep the pick goes below the plane of the strings; and your wrist action together with how you hold the pick. 

Thicker pick with less of it sticking out of your fist (and not going deep below the string plane) usually go a long way towards solving the CLICK.  

Still, your hand/wrist action is an important part of controlling the sound of the pick.  If you are holding the pick rigidly upright like this: |   as you strum across the strings, the drag as the pick passes each string and releases it -- causes the dreaded CLICK.  If instead, you rotate your wrist and the "attack" of the pick, you'll get a lot softer sound.  As you strum outward and inward, rotate your wrist a bit in each direction so that the pick slips or brushes across strings rather than digging into them.  Like this:  /outward and this:  \inward only even flatter angles...  

You can try a thicker pick to soften that pick clicking noise.  Or you can try angling the pick differently.
Some people (myself included) actually like that pick clicking/percussion effect and use it as part of our personal playing sound.  One person's "bad habit" may be another person's 'bonus effect'! 

I'm learning to play quickly after almost 50 years with other stringed instruments, but it feels like I may be developing a bad habit.  When I strum with a thin triangular pick over the lower bout sound holes to get a sweeter tone, I'm also getting a consistent click from the pick striking the fretboard. 

I watched a very experienced player recently and noticed some clicking from him, too.  Is that sound just inevitable, or is there a technique I should be using to minimize pick click when I'm not strumming over the scooped portion of the instrument?

Thanks for any advice!