Handloading for the K31, or any other of the Swiss rifles/carbines designed for GP11 ammunition, is made a lot easier by the fact that it shoots a .308" bullet, just like the, uh, .308Win. Choosing from the vast range of bullets from 155gr up to 180gr is part of the fun, and over on swissrifles.com our own diopter has put together the vast majority of bullet/powder combinations in one very comprehensive thread.
Cartridge cases from Prvi/Wolf/Graf make easy loading, a required exercise, since GP11 is Berdan-primed, sadly. Notwithstanding that, the quality of the brass is extremely high, maybe as good as or even better than Lapua/Norma brass. I bleeve that Trade-ex is a major source of components, and Brownells are the to-go source of the many worthwhile accessories made by our friends, Swiss Products, down there in Kallispel Montana.
Although the choice is rather limited for the 6.5x55SE, the same Prvi/Wolf empties are not that hard to find, and the bullet weights, though limited to 120/123gr and 139/140/160gr, make an easy to shoot gentle recoiling round that can be shot all day by most shooters without discomfort.
Both calibres are astonishingly accurate - the K31 with the misurp GP11, and the Swde with good handloads - in fact, the 6.5x55 was for many years THE 300m match and biathlon calibre. When that was my sport, taking part in Norway was great fun with the 6.5x55 Kongsbergs we used to get given for the comps. Over on another forum, one keen Swiss-schtuff shooter developing handloads has been posting 12" groups at 1000 yards...with a 168gr SMK and a GP11-simulating load of RL17.
Buy either, or better, both, like I did, and enjoy the look on your fellow shooters' faces when you clean their clocks for them with your old-fashioned wood and tin milsurp.
tac