All H&R stocks will fit all of their break barrel firearms. I think the 2" shorter BC carbine forend will look better on the 22" barrel than the longer BC/Target forend in case you want to check that out. The checkered walnut Topper Deluxe Classic stock is also available if you don't want the steel butt plate. Lots of choices.
Click HERE for 5 pages of Handi pics, you may see something else you like.
TDC stock bottom
BC Carbine stock bottom
BC Butt w/recoil pad, TDC forend