Local gun stores, gun shows, dealers in C&R type stuff on-line.
You can get Swiss GP11 ammo, Hornady makes ammo, Norma makes ammo, and there are a few other off brands.
Of course I handload for mine. You get the brass from Norma, or Graff's. It has a .308 bore, so you use the same bullets you would for a .308/.30-06 rifle. These rifles were designed for the GP11 cartridge which is a 174 grain bullet. Luckily Sierra makes their famous Match King in a 174 grain .30.
You can find out where people are buying ammo, where people are buying rifles, loading data, history, etc. on the many boards that cater either to Swiss rifles exclusively or on the various C&R boards.
I know this is your rifle and you can do with your property as you see fit, but I really hate to hear about people doing "ninja modifications" to them. The K31 is a fine old rifle. It still shoots just as good today as it ever did. You can have a lot of fun with it. My 2 cents that you didn't ask for is to leave it alone. If you want some kind of tactical rifle, there are plenty of new ones out there that don't have any history behind them.