Radio frequencies in the USA are assigned by the FCC, not the FAA. There's no 'private' air-to-ground frequency mentioned in the AIM but section 4-1-11 does say that the FCC has assigned 122.900 as a MULTICOM frequency for:
Activities of a temporary, seasonal, emergency nature or search and
rescue, as well as, airports with no tower, FSS, or UNICOM
Arguably your fly-by is "temporary activity", however the definition of MULTICOM is:
A mobile service not open to public correspondence used to provide
communications essential to conduct the activities being performed by
or directed from private aircraft
So if your fly-by is "essential" (and safe!) then I guess you could use 122.9. There are procedures for requesting temporary air-to-ground frequencies for air shows, but that's obviously a special case.
As for legality, it seems that you need an FCC license to use an aviation handheld radio on the ground:
You may only use your hand-held aircraft VHF radio in your aircraft
under the terms of your aircraft license. You are required to have a
separate Ground Station license to operate your radio on the ground.
But because this is more about FCC regulations than FAA ones, I suggest that you ask on ham.SE; they'll probably know a lot more about how it all works.