Ah, the dreaded M-96 Swede, one of my favorite guns of all time. PO Ackley said of the 96 (94, 96, 38 all same) that it was the safest action of the 95 Mauser types, having a firing pin collar and a gas port. PO also noted in his books that gunsmiths were making custom 22-250 guns from the 96 action. However PO thought that the practice was borderline.
You already have what amounts to a 260 and a chambering that might well be the closest thing we will ever see to the "do-all rifle." The Swedes use the 6.5x55 to shoot everything from rabbits to moose. It will shoot sub 1/2 inch groups; it will do 3,500 fps with an 85 Sierra as a varmint rifle and near 3,000 fps with a Hornady 140 as a deer rifle. If you stick a 160 in it, especially the cooper nickel FMJs it can be used to shoot tanks or roaming APCs.
Don't be sidetracked by the SAMMI penchant for down grading European guns/cartridges. The Swede is made from the very best steel. When a contract was made with Obendorf of Germany to produce guns for Sweden, the Swedes sent their steel to Germany to have their rifles built from. They did not like or trust the German steel!
Best,
Ed