03a4 rebarrel to 9.3x62

Just a new barrel of have the original rebored.

Reboring is possible. Bigger hole will make for a lighter gun and a heavier bullet, might be a bit of a kicker but as a hunting rifle, so what?
http://www.35caliber.com/8.html

No action work was necessary 8 years ago.
30-06 to 9.3x62

Now let's talk about your 1903A4. Just how extensively was it sporterized? Barrel cut off, turned down, polished shiny? Action drilled and tapped for something besides old style Redfield JR?
There is some interest and value in "re-miling" sporterized military rifles that have not had the basic structure of barrels and action cut up; and an A4 would be one of the best.

Head size is the same (within manufacturing tolerances) and the length of the case is within a millimeter. So rebarreling or reboring would be fairly straightforward. The only difficulty I can imagine is the shape of the 9.3mm bullets. Most likely, the bullets would move through the action without comment, but even so, a rather minor amount of fitting should settle things out.

May I point out the 9.3x62mm is the European answer to the .35 Whelen. The 9.3mm uses a heavier bullet and is slightly larger in diameter. Ammo is much more costly or requires reloading.

I've read about 30-06 BAR's (not the military version) being rebored for 9.3X62mm use - a semiautomatic 9.3X62mm isn't something I'd pick but some have!

03's are known to split stocks w heavy caliber rounds. Might want to use an aftermarket stock.