There is no chance to get it back as a historical weapon.
It is an unregistered NFA class firearm. It is contraband.
There is no program in place to now register a previously unregistered NFA firearm.
The Handy Gun has not been removed from their NFA class by the BATF as the short barreled Winchester & Marlin 'trapper' rifles & the shoulder stocked Luger and Mauser pistols have.

If it were a full auto firearm or a silencer, no options would be given to deactivate or alter to allow them to be returned to their owner.
The H&R Handy Gun is specificly listed & illistrated as an example of the AOW by the BATF.

Either take it as modified to meet the handgun or shotgun Type I firearm classification they specify, or loose it altogether by forfeiture to L/E.

I'd take Dad's Handy Gun w/a CF liner in the bbl. It won't change anything on the outside of the gun. It'll be a bit heavier for sure!
But it won't be a manhole cover in Bloomberg-ville.
JMHO