I had this done to me once, but the frame was Italian, so both sides had right-handed threading.

I assume yours is too, or you would not have a useable frame. (The BB cups can't be BSA -- even the right-threaded one won't work as it is a different diameter and pitch.)

When I finally got around to correcting it 25 years later, I remember it was an ordeal to get the fixed cup off, but the frame and threads are fine.