If you can find brass, you'd be ok. Once fired or new would work, as you can reload these. Search the internet and gun sites for it and place some WTB adds for the brass. If you can't find the brass to make ammo, then a caliber change would be needed. (I'm seeing the same issue with the 25 WSSM stuff)
First, I'd find out if the M70 WSSM action is shorter than a standard 308 action? If it is a shorter action, than that limits you to 223 length rounds (about 2.250"), and not 308 Win length rounds (about 2.800"). If it's a standard short action (308 Win length), you will need to change out the bolt to the proper bolt face size you plan to change to. 223 size or 308 size bolt face. If you change to a smaller diameter round (which is most likely), you will need to upgrade the magazine to feed the smaller rounds. So, it depends on what size of action you really have. Either way, you will have to upgrade the bolt, and magazine system.
On the barrel, if you plan to keep a .224" caliber and you have enough barrel shank left at the chamber end, you can reuse the factory barrel. You will need at least 1.4" to 1.6" of remaining shank to rechamber the factory barrel, maybe more depending on the caliber you go to. Only a gunsmith can tell you this. First is to find out the size of the action. The Rem 700 actions are the same length for a 223 and 308. I just don't know enough about the M70 actions when it comes to the WSSM size case in that rifle.