Goodtime: Welcome aboard!
No! The bolts on the large ring and the small ring Mausers are not interchangable, just like Richard (AtlLaw) is not irrascible.....wives and in-laws aside, although there have been a few times when.....well, I s'pose I shouldn't go there........
If you need a bolt for a Mauser rifle you need to match it by model (93, 95, 96, 98) and even country of order - Spain, Argentina, Chile, Turkey, etc.
If you're not too keen on this stuff then corral your local gunsmith to give you a hand. HTH.