Considering the number of Mosin M44 on the market I do not see any reason not to refinish using the product of your choice.
If you had something that was not as common then I would recommend keeping the original finish.
I've cleaned up dozens of mil-surps with BLO.
I have a few K31's and I would like to refinish one in multi coats of Tung oil after stripping and bleaching the wood. This particular K had damage at the muzzle and the best recourse was the turn a new crown and then thread the barrel for a muzzle devise. Being no longer original it's a great candidate for a non military finish.
I think this one would look good with a higher gloss wood finish.