Yes, I know some players prefer an oil finish on their sneaky pete. It is not really a durable or hard finish, but I know a lot of players prefer that.
You may send it back to Jimmy to get him to remove the finish for you, and treat it with an oil finish or something like that.
If you want, you can try to install a wrap. Leather seems to be better for those with a sweaty hand.
Please make sure you get the wrap done by someone with a lathe with a tapering bar so the taper of the butt will not be cut inproperly.
You can also buy a slip on rubber grip to slip on your handle, it is quite inexpensive. It will make the butt a bit thicker but not by a lot. That is the most inexpensive option I can think of.
Hope this helps.
Richard