Seems I recall Hornady recommended not loading the K31 in it's original configuration to maximum since it has a weak action and unsupported chamber. Based on that I'd assume the higher pressure cartridges you are considering might be a bad choice.
Hopefully someone more familar with those rifles will weigh in here.
As long as you have a K-31 that was upgraded in 1911 (if it is a 7.5x55 Schmidt Ruben) then that round is already very close to being a .308's twin. There should be no problem rechambering to either of those calibers providing you have a good smith do the work and don't use max pressure loads. Do a few google searches and you should find some information on this subject.
K31s have a fully supported chamber. That warning was for 1911 and older models. Civilian K31s were chambered in 308, 30-06, and 300WM. They are plenty strong and safe. Commercial hunting ammo is available from Privi and Hornady.
A lot of the fears propagated about straight pull rifles really don't apply to the K31 and probably come from horror stories concerning the Ross rifle. If you reload the 7.5 Swiss in a K31 is essentially the same performance as a 308, perhaps better with heavier bullets. The real issue with rechambering these rifles is the helical locking lugs. Typically a new barrel is attached to a stub from the existing barrel. Go to Swissrifles.com and you should get some good advice.
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