I’m not familiar with nylon tape wound, but I am familiar with metal tape wound — and with nylon wrapped flats for bass, as well as classical guitar strings. I don’t care for nylon strings. They stretch too much and require fiddling with the tuning.  I also don’t care for the sound — they’re too mellow; YMMV. If I had an issue with string squeak, I’d probably look at either nickel flats or tapes. For me, they produce a livelier tone.  

I got mine from strings by mail.

Thanks for the specific recommendations, @skip.  The D'Addario option is similar to my current string (La Bella), but I'll try to locate one of those flatwound strings you mention.  I'd prefer not buy a whole set since I only need one string, but if it will work I'm not opposed to the idea.

@Strumelia, that's good advice, and I already have the specific gauges used by the builder, who, incidentally, is also creating an alternative bridge for me should I choose to string the dulcimer with steel strings.

An "occasional squeak" would not be objectionable. I find it a nice reminder that making music is a tactile experience.  But one of my philosophies of dulcimer playing has been to keep your fingers down as you move from one chord position to another to facilitate a fast and smooth transition.  That strategy is not working on this dulcimer, at least not on the bass string at present. I find myself re-evaluating my technique.

If/when you do order more nylon strings, keep in mind that depending on what note you are aiming to tune to, the thickness of nylon strings suitable for a given note won't be the same thickness as for metal strings... so you may not want to order solely by gauges we commonly use with metal strings. But I'm sure the maker has advised you on the nylon strings needed for its current setup.

I have to say that i personally enjoy the occasional squeak of a wound string. I listen to a lot of classical lute music and I like that about it- makes it feel more alive and richly textured, like the musician is sitting right there with me while playing.

There are some flatwound, nylon core strings being used by the ukulele community. I think they are used on classical guitars. Thomastic Flatwound .027 & .030 is one, there are others.

https://forum.ukuleleunderground.com 

Edit:

D'Addario has some strings that may work also. NYL028W [melody on my Blue Lion bass]

I have some of their PB023/PB024 phosphor bronze I haven't tried yet.

You may need to use fingernail polish/superglue at any cut line.

@dwain-wilder, I've already started adjusting my technique by lifting up any finger on the bass string before moving to a new chord position.  It's a challenge, though, for on the dulcimer we slide much more than do classical guitarists who have a greater range of notes in any left-hand position than do we.

Thanks for your comments, @matt-berg. It's a really special instrument.  Bob Stephens has some really innovative design principles.  The instrument sounds incredibly soft and warm and the intonation is spot on. I'm still figuring out what tunes sound best on it.

Dusty Turtle,  I do not have a solution to your bass string squeak.  I do want to congratulate you on getting a Stephen Dulcimer.  I have had the opportunity to talk with Bob about lutherie and was blown away by what he builds.  Enjoy your new instrument.  Matt

Classical guitarists deal with this issue by learning to handle the wound strings differently, and accepting a little squeak as part of the instrument. Kind of like accepting that a pipe organ will have some "chuff."

There are squeakless strings, though.

Thanks, @stumelia and @nate. One issue I have is that were I to move to a non-wound string that was thicker, I'd need to adjust the groove cut in the bridge, something I am not eager to do just yet.

Those string lubricant products are very strange. The feel is totally different. I think a lot of them are mainly just mineral oil. Personally, I like it, but can't be bothered to apply a product to my strings before playing. Heck, I can barely even be bothered to tune up xD
Sounds like a thicker unwound string is the way to go. I will have to check out that brand as well.

Dusty, Nylgut brand (sort of imitation gut strings but made of nylon) strings for banjos have some sets with thick nylon bass strings that are solid nylon, with no outer winding. They never seem to break for me, and have a wonderful resonant sound. I prefer them on my nylon strung banjos. Banjos have basically the same length strings as dulcimers, so you could check out a set from them. I know of three types of banjo sets Nylgut makes- Minstrel (for lower tunings, slightly heavier), Classic (thinner, work well for higher tension oldtime tunings), and they also some sets with 'red' strings that some folks really like but i have never tried those and don't know what advantage they might have. I highly recommend Nylgut strings. Long ago I used classical guitar nylon strings on my banjos, they were quite heavy and broke much more often than my nylguts.
Once I bought a used banjo that had Nylgut strings on it that had not been changed in over 10 years. I figured I ought to put a fresh set on, but when i played it, the old Nylgut strings sounded just wonderful and i played on them for two more years before i then sold that banjo... with the same strings still on it of course.      Just sayin'!

I just received a beautiful new dulcimer by Stephens Lutherie built with nylon strings.  The sound is incredibly gentle, round, and warm, and I am overcome with the desire to play lullabies and other soft music.

However, the bass string is a wound string and squeaks a lot. Because the nylon strings are quieter than steel strings, the squeak is much more noticeable than on steel strings (but even on my other dulcimers I use flat wound strings to reduce the squeak).  Dulcimer playing involves a lot more sliding than does guitar playing, so it is likely that the squeaking is much less of a problem for classical guitar players.

Any remedies?

I do see that there is something called "tape wound" nylon strings.  Does anyone have experience with those?

Additionally, some classical guitar discussions online mention using Fast Fret or Finger Ease to smooth the friction of the strings.  I am not eager to start using such a substance on my instrument, but perhaps I could isolate its use to the base string.

Any thoughts?