.260 Rem might be a pretty good suggestion. Performance is pretty close for the two of them, but in the future brass *might* become scarce for the 6.5x55. With .260 Remington you can always form brass from .308, which will be around a LONG time. Plus if the US ever enacts one of those insane "no military calibers for civilians" laws, then .260 Rem will still be legal, whilst 6.5 Swede wouldn't (of course .308 would be gone too then, but I guess you could always neck up .243 cases).
Of course, for a slightly cheaper route, you may (I say may because I've not consulted a gunsmith on this) be able to have your rifle rechambered and rebored (keeping the same barrel) to 7.5x55 Swiss. I'm not sure if the M96 action can take the pressure though.