John is correct, old steel doesn't degrade, but years of shooting can put wear and tear on an old action. We have no way to know how hot the loads were that have been shot in any gun over 100 years old, as most of the previous owners are long gone!
Still, if all looks tight, and the gun checks out good, the loads you are planning to use should be safe.
I shot my Swede Roller, which was made from a US made Remington action, chambered for the 12.7 cartridge, and it saw a lot of smokeless rounds.
My new Rolling Block is a #1 Sporter in .44 Sharps Bottleneck, and it too will have some mild smokeless loads run through it.