Carcanos are funny creatures. Military ball that I have is in the neighborhood of .266" +.
Right now, in 6.5 X 52 Carcano I am regularly shooting the following: M-1891 Infantry rifle, M-1941 Infantry rifle, M-1938 Short Rifle, M-91/38 TS carbine and a M-91/38 Cavalry carbine. Strangely, 4 of the 6 shoot exceptionally with Hornady .264" 160gr RNSP, but 2 of them require a .268" version in order to get decent accuracy.
My advice is try some .264" first. If your rifle likes them, no need to go to the .268". In fact, I'd recommend that you NOT go there.
Hornady 160gr RNSP will always outperform any other 6.5 because it is a looooong, flat sided bullet and it has a flat base.
Also remember that you want to bury the front sight blade into the very bottom of the rear "V" ... if at 100 yards or less ... aim for the belt buckle and you'll hit the target clearly in the chest.