Since those stocks are already refinished, you will do no harm by restoring them. It's not difficult if you have any aptitude at working with wood. Main thing you need is a single-line checkering cutter from Brownells, a set of riffler files, some tung oil, and bit of patience.
Strip off the finish, fresh out the checkering with the single-line cutter following the original grooves, deepen the border cut with a square riffler if it needs it (doesn't look like it does), and then put on 3 or 4 coats of tung oil according to the instructions. Tung oil will not fill the checkering like other finishes.
I did a set for my M28 to replace the rubber Hogues that came on it, after cutting them down to fit my little girlie-man hands. They look just like new. I am now working on a set from a 1949-vintage K-38 that were done the same way yours were before I got it.