Henry, I've refinished a few. But apart from one which had had ebony dye applied to it before I got it, I don't use dye on them. I simply sand them smooth and then oil-finish them with tung oil. Once in awhile I'll use artist's shellac on one.
The oil-finish process is slow and requires patience. You have to oil the stock every day for a month, rubbing in the oil with your bare hand. The finish isn't slick, as it is with a varnish or even shellac. (Please don't mention polyurethane in connection with stocks; I get violent.) But when you're done, it has a silky feel that is very pleasant to the hand and in my experience won't slip if your hand gets sweaty.
The trick with any finish, I've found, is many thin coats, lightly sanded or rubbed down between coats. I tend to treat them the way I do antique furniture, guided by Her Imperial Majesty, oddly enough. One summer while she was in high school, she and her BFF spent a summer working for an antique furniture refinisher, stripping and refinishing furniture. It was from her I learned the trick of rubbing down the wood with a coarse linen rag instead of fine sandpaper. The linen doesn't leave abrasive residue behind it, but it does require more work on your part. As I find oil finishing therapeutic, I don't begrudge the time it takes to do it right.