I'v found nylon picks [I use Herdums] don't make as much of a click as plastic ones.
Fixing a loud strum
Michael, what you are referring to is called pick clack. It is more pronounced with thinner picks, so you might try heavier picks. Heavier strings, and a softer strum.
And make sure you are not hitting the fretboard with your pick. Just strum or pick across the top of the strings.
When you strum you don't want the pick to get down into the strings but merely skim the top of them. Angle the pick ever so slightly so that the tip points toward you when you strum out and away from you when you strum in. Also, angle the pick ever so slightly so that it is the edge of the pick that hits the strings. Assuming you are right-handed, the left edge should hit the strings when you strum out and the right edge should do so when you strum in. These techniques minimize the amount of the pick that comes into contact with the strings.
One final question. Where was the microphone when you recorded yourself? Conventional wisdom is that pick clack sounds louder to the performer than it does the listener. You can test that by putting the mic right in front of the dulcimer and recording yourself, then moving the mic progressively further away and seeing what happens. Presumably, the notes will ring out louder than the pick clack, so that the further from the instrument the listener is the less noticeable is the pick clack.
Dusty T., Northern California
As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie
updated by @dusty-turtle: 05/17/16 12:39:15AM
I just recorded myself for the first time and I was surprised by how loud my strum is. It was loud enough that it could pass as accompanying percussion! In case I am not using the proper term I am specifically referring to a clicking noise that is coming from the pick hitting the strings. I tried a thinner pick (although the thinnest that I have is .60) and it didn't help much. Anyone have any thoughts on reducing the strum noise?