The tuning pegs work exactly like the ones on a fiddle, and the proper method is to "unseat" the peg by pulling it out of the hole slightly. Something like a sixteenth of an inch or less will generally be enough to let the peg turn "almost like free." Then you're pulling against only the string tension. When you get the pitch you wnat, a little push back into the hole should seat the peg so that it holds.

Depending on the tuning, the string tension on a dulcie likely will be a little more than for a fiddle, but shouldn't be unmanageable unless your arthritis is fairly advanced.

Trying to turn the peg while it's fully seated can be really difficult - especially if the peg and hole are well fitted. It also wears out both the hole and the peg.

The peg dope already mentioned does help make things work smoother.

If you "back off" the string tension while "unseating" the peg, it may be easier, and you can brace the heel of the hand against the instrument to "lever" the pin out so that forces on the wrist are minimal. If the arthritis is mainly in the finger joints, you may still have some difficulty.

When you push back in to seat the peg, you only need enough "push" to hold things in tune, so with reasonably well-fitted pegs it shouldn't be too hard.

If you do decide to go with gears, the planetary type (often called "banjo tuners") are frequently enough used on dulcimers to look "almost traditional" to most, and although they usually require a little larger hole than the pegs, they don't "deface" the instrument with the screw holes you need for "guitar style" tuners. They also tend to work a lot smoother and are adjustable so you can get "just enough" holding with minimal turning resistance.

Since any instrument with pegs eventually will "wear out the holes" and require plugging and re-boring, plugging the slightly bigger holes needed for the banjo tuners is theoretically possible should you decide to go back to pegs. The dulcie then will just look like it was "worn out once" and was repaired - if you can find a capable repair person to make the fix for you. If that's really important to you, I'd suggest discussing how well it would work on your particular instrument with a good shop before proceeding; but unless it's a very old and/or "rare" instrument the change to good tuners shouldn't harm it - much.

John