The large ring Mauser shank diameter is 1.10", the '03 is 1.04'. That is not enough to cleanup the threads.
Pre-threaded barrels for the M1903 are hard to find, but any competent gunsmith should be able to fit a 7mm barrel on that action with no problems.
I strongly advise against playing around with welding and bushings. The last time I checked Brownells, eyeballs and fingers were backordered and might not be available.