What I would do....is photograph the gun and any numbers and put them away. If it/they get stolen...you can report the actual gun.
This is what people should be told to do. IMHO
Same story....Criminals aren’t going to register them.
HAYNES v. UNITED STATES, 390 U.S. 85 (1968)
http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?court=us&vol=390&invol=85