Your thread caught my eye as I've been dealing the last year or so with increasing arthritis in both hands. I have a particular problem with loss of flexibility in my left index finger, making it difficult to play my fiddle and guitar as a I used to. I happen to have a mountain dulcimer as well, although I've only ever noodled around with that, and don't play it extensively. I can still play that, because I hold it on my lap with my hands coming from above, so no need to bend my left index finger.

From your description, it sounds like you could probably manage well with your left hand, in terms of fingering chords or single notes on the dulcimer. I can't tell, based on your description of your right hand how much you could do. Do you feel strumming with either your hand or a pick would be comfortable for you? Is there any possibility of trying out a dulcimer before buying to see how you do?