First, the gun. If the case with the oversized bullet won't go into the chamber... forget it. If it will, as suggested, pressure might be a bit higher. Strong possibility in commercial guns. Custom chambers, less likely.
Mr. Ackley in his books tells of an experiment. Silly fools were buying surplus 8mm to shoot in Springfields (yes, .30/'06. "Well, all soldier rifles shoot the same ammo? Don't they???" Ah... no...) He rechambered a .30 barrel to 8x57. No problems firing surplus 8x57 ammo. Accuracy wasn't. No big notice in pressure change. The Springfields that "blew up" were "cut up" by escaping gas from the 8x57 case that split because it wasn't supported.
If you are going to do a big bunch or desire great precision (ha, ha), corbin and others, ch4d.com for example, sell a "ring die" that most presses permit you to shove the bullet in and come out the smaller size. Classic high pressure lubes are lanolin, any drug store, or castor oil. Or you can mix them...
A cast bullet resize die is going to be worked beyond its design limits by a jacketed bullet but well lubed, lot cheaper than the ring dies. And if ou break one, might not break the next as soon... Your budget.
You will get some "core bleed." It squirts out. This small reduction shouldn't be a problem. Mr. Corbin has pictures of .323 to .318 in his books.
and you don't do this to make target grade bullets. They will go bang, but ... enjoy, luck.