Well, back in 1937, Sharpe wrote about using .32 caliber pistol bullets in the Krag & '06.  There is no reason why the Carbine bullets would not work for you. 

GI Carbine ammo was loaded with non-corrosive primers from the very start, so no worries there.  The GI ammo was supposed to be loaded with ball powder.  When you pull the bullets, you can salvage the powder.  But check every load you pull.  The powders & charges may be different, but may well work as a minimal load in a Krag. 

Give the carbine cases away.  Some pilgrim will want them.