The new barrel would need to be cut, threaded, chambered, headspaced, and cut for the extractor relief --as with all barrels. Mounting/clocking the sights, too. Since 7.62x54R doesn't really need the bolt, extractor, or even clips to be modified, I suppose there's no reason you couldn't make switch barrels for both.
After all that trouble, though, there's not much point in shooting 8x56R, though. It's not a particularly awesome cartridge, or anything, and is mostly rare and expensive. Switching between a long/heavy barrel for a short light one could be pretty cool, but would be a pretty ambitious undertaking.
Depending on your woodworking skill, I'd look into a Boyds stock blank to see if it could be made to work. If they have one that has no inletting but the barrel channel done, you'll be set. Whatever you do, examine the existing stock for design tips; there's a metal reinforcement to spread the load of the tiny recoil lug, and several crossbolts to keep the stock from splitting.
For now, I'd buy several boxes of 8x56r, a slip on buttpad, a pillow for a cheek rest, and see if the rear sight can be replaced with a peep. Unless you have a specific end goal in mind for the gun from the get go, permanent modifications are a bad idea. After a goodly amount of shooting, you'll be able to decide exactly what you want changed (the stupid sling swivel being the first, no doubt), and what role you'd like the rifle fill.
The sling swivel and its lack of a real grip surface are the two biggest problems most run into that can't be readily solved. Possibly some grip tape judiciously applied to build up the grip area might help, as would making a spanner wrench to remove the sling swivel (or just cut it off)
TCB