The barrel would be made by the Swiss military contractors--there might be some sporter barrels made in Switzerland but they are not available here except maybe as an imported whole rifle. The machining cuts on the k31 barrel breech end makes it difficult to alter issued barrels for converting cartridges without some pretty good machining skills due to the Swiss manufacturing precision. The one guy that does it in the U.S. uses old bored out K31 barrel stubs at the breech for their machining cuts to enclose a new barrel chambered in whatever cartridges fit the action. There is some discussion at the above link. The k31 bolt sleeves do allow some adjustment of bolt headspacing which is less of a problem than the specific barrel design. The 1911 and prior models of Swiss rifles are far easier to convert and their barrels can be set back/rechambered due to a relatively simple breech design but see below.
See Swiss rifle Q/A at
http://swissrifles.com/sr/faq/
"Q. What about the K31s you mentioned in .308 and 30-06? Can I get one of those?If you can find one, sure. Just be sure of the source. Several companies, including Grünig & Elmiger (
https://www.facebook.com/pages/Grünig-Elmiger/561040110594791) and Hämmerli, used Schmidt type actions to produce sporting rifles in a variety of calibers. However, a number of 1911 rifles were converted to the .308 round in the 1960s. The 7.5x55 cartridge generates approximately 45,000 psi, .308 cartridges can generate well over 50,000 psi. If someone did a shoddy rechambering job, the results could be tragic."
Here is a picture of a rare Hammerli .22 LR designed to look and feel like a K31 rifle
https://www.tapatalk.com/groups/theswissriflesdotcommessageboard/haemmerli-kksd-551-t8122.html
https://www.tapatalk.com/groups/the...k31-rifles-in-the-early-1970s-t10885-s10.html
And a G&E match rifle made in .308 for shooting competitions
https://www.tapatalk.com/groups/the...-and-elmiger-cism-rifle-in-7-62x51-t3709.html
Given that 7.5 Swiss brass and .308 bullets can be now be purchased reasonably and handloaded to effectiveness, there is little reason, to rechamber these rifles in .308. Very little performance is to be gained and it is easy to compromise safety and reliability. Heck, even the magazines are going for over $50 for replacements and $100 or more for the original mags--bugger one up and they are hard to replace.