Re: Mauser 6.35 (1910) & Colt D.A 38
You don't say what state you are in, but in most states there is no requirement to register firearms, New York, New Jersey, and some others being exceptions. There is no federal requirement for registering ordinary handguns like those, only for machineguns, short barrel rifles/shotguns and a few other weapons. If your police department didn't know about state or local registration requirements, there probably are none.
As to evaluation, the Colt is either the New Navy or the New Army and Navy, and dates to the 1890's or early 1900's. The Mauser is as you say. Unfortunately, both pictures are so poor that any evaluation based on them would be impossible. In evaluating any firearm, condition is all important and without better pictures there is no way of determining condition.