I don't see any need to re-case harden it. You don't want case colors on the engraved surfaces. You still have the original case hardness,,however deep it is, on the internal and wear surfaces where it is actually needed.
Adding case hardness back to the engraved surfaces,,regardless of colors , isn't going to add much to the strength of the frame.
There wasn't much case hardness in that one to begin with from the sounds of it anyway. Some don't have any at all, just colors.

I've done a few in that manner (polishing the outer surfaces & engrave) and then french grayed the surface afterward.

Firearms are engraved thru the case hardening all the time. The quality of the engraving haveing been done so varys greatly however.