People are still building short barrel rifles. I would guess, but am not sure, that if it was shortened after leaving the factory, it could till be registered.
As a precaution, you could pull the barrel off of it until you get it sorted out. Pulling a barrel isnt rocket science, tho decent tools is best. It's a 10 minute job for a 'smith. Last one I had swapped by a 'smith cost $15
You could also get an original standard length barrel from the time period and screw it in. Without a letter from the Cody Museum, it's hard to say if its orginal, tho the length is odd. Are you measuring from the back end of the chamber, or the front end of the receiver?
It would be more valuable than a standard gun if that was the original length from the factory. If it was done after leaving the factory, the value is decreased from a standard gun, and probably wouldnt be worth registering. It would be worth more rebarreled with a standard barrel.