Who... me?
Though I do perk up at any mention of der Mannlicher Schoenauer I haven't much to add on this one.
I've never owned or fired an MS stutzen in 6.5 but have read that recoil is light and they are, of course, light and handy with legendary smoothness of operation and are supremely 'pointable' (stock engineered for 'snap shooting') as is my M1910 (9.5X57) Take Down Model.
That said, the advice of so many lifelong hunters here regarding rifles with which they have years of personal experiences far outweighs any speculation I may have regarding the OP's situation.
I have profound respect and admiration for Mannlicher Schoenauers, particularly those of the pre WW2 period, but would that make one an ideal rifle for Billy? The fact that the Schoenauer magazine of an M1903 performs flawlessly _only when fed cartridges at or very near to original profile_ limits the type of ammunition used and availability of same can be an issue.