K31's and Swedish Mausers are largely considered the most accurate of milsurp rifles. Great triggers and overall outstanding quality. Via the K31, I've won a bunch of trinkets at local matches plus some silver medals at the annual CMP match at Camp Ethan Allen. The straight pull bolt is great for the rapid fire stages. I think the K31 might have the most Vintage Military Rifle wins at Camp Perry Nationals over the last 10 years or so.
Check under the butt plate to see if there is a troop tag. One of my K31's that I shoot most often in vintage matches was shot in the Swiss national Schuetzenfests by the same guy it was issued to in the service. The name on the troop tag under the butt plate matches the civilian business sticker and the Schuetzenfest sticker. There's a stack of Schuetzenfest inspection stickers on the hand guard.
FYI, so far I have not found any new manufacture stripper clips that are worth a sh!t. Also the reproduction magazines are OK except for the latch pivot pins that like to fall out. Peen the ends of the pin a little and it will stay in place.
IMHO worth getting your hands on a little GP11 to at least try it in your K31. I spent a lot of time trying to develop a load that would beat GP11 and the best I could do was achieve similar results. PPU ammo is decent.