This may sound like a stupid question, but I have looked and cannot find a "simple" answer...

I am in possession of a 700 LS with an after market barrel in 35 Whelen, but the barrel is not marked. (I know the caliber as I have fired the rifle.) Did the gunsmith break a law by not engraving or stamping the barrel?

Additionally, is there the potential for stressing the barrel by having it stamped, and if so, would engraving it be better?

If an individual put the barrel on, no need for any markings. Manufacturers do need to mark them.. Stamping is fine. Have you not seen factory barrels with rolled on markings? And millions of custom barrels with stamped markings? If you want it marked you should do it. otherwise, forget it. But always good to have markings for future owners; so they know which ammo to feed it.

The answers to your two questions are "no" and "no".