Dave the book I referenced is very clear that the 375 ammo should not be fired in any weapon except thoose chambered for the round. I understand where your coming from with the antique guns and that is often the case with lever gun ammo being loaded so mild however in "Cartridges of the World" they address that issue with the 375 as well and say something to the effect that using the 375 ammo in a vintage 38-55 would almost certainly result in dissaterous consequences. Hope that helps and it probably falls under the category of you might get lucky and you might have a big problem. Not worth the risk IMO. Try ordering the BB ammo from Cabelas. They have it cataloged and most likely in stock.
