Up until serial no. 800,000 the recievers of theM1903 were case hardened, and occasionally the case hardening was allowed to penetrate too far into the steel, leaving the reciever brittle and subject to breaking or cracking. At serial 800,000 the heat treatment was changed and the problem eliminated. Later the type of steel used was changed to a nickel steel alloy, and those (I think it was about serial no. 1,200,000) are considered the strongest M1903's. During WW2 some of the old M1903's under 800,000 were pulled out of storage, rebarrelled, and the bolts were replaced with later nickel steel pieces. It sounds like you've got one of those units.
Now this is just my opinion, and I've not seen your weapon, but my hunch is that, if the reciever hasn't cracked by now, it ain't going to. If you're willing to have the reciever checked for internal cracks, and it shows up OK, and you stick with factory loaded '06 ammo, you're probably going to be OK.
Check with metal shop about magnafluxing or x-raying the reciever.
For the record, the bulk of the M1903 's carried by our troops in WW1 were pre 800,000 guns, so they're not time bombs; but that reciever is over 80 years old, and until you can determine that it doesn't have any cracks, internal or external, you can't be 100% sure about it.