Ahh - one of my favourite topics! My advice would be to try every material you can get your hands on. Try every type of grip. Try every strumming style/direction.
I'm constantly looking for the right tone and feel for each piece of music I play and each situation I play it. Before I record a piece of music I'll have gone through at least half a dozen right hand options for picks and strumming styles to find THE tone for that piece of music at that time. I think that developing your own tone is fundamental to learning the instrument.
I have a number of 'picks' in my box including off-cuts of boot leather shaped and sanded in various ways, thick goose quill ends in various cuts or uncut, pieces of wood made into strummers, long 'whipping' quills and, of course, the thumb strum. I also carry a few guitar picks of various grades but rarely use them (although I do in some situations, particularly when playing chord melody tunes in DAd).
Leather can give a nice rounded tone but it all depends on how the piece is shaped (as with all picks). I get free off-cuts from our local shoe repair shop.
The three right hand techniques I use the most because they usually give me the best tone for my style of playing are the vertical quill butt, the horizontal whipped quill and the thumb strum. A good percentage of early dulcimer players used these techniques a lot too - because of the tone they generate for noter drone playing.
So I would recommend spending a lot of your practice time trying different picks and strumming styles.
Try this experiment: Put your right hand behind your back and hold down a note or chord with your left hand - listen to your dulcimer. Then put your left hand behind your back and strum your dulcimer with a pick in your right hand - listen to your dulcimer. From that you can decide which of your hands it is that actually makes the sound come from your instrument - and that's the hand you want to spend 90% of your time developing
(You've got it! In general we spend all our time focussing on the wrong hand when we practice!!!!!)
Robin