OK, let me see if I can help clear up some of this. Remember I am not an attorney.
All 40mm are restricked and require register papwork unless they are demilled and rendered useless. The exception to the rule is a 40mm with a 37mm non-rifled barrel which would be a tittle one firearm. Most 37mm's do not require paperwork unless they are in possession with anti personel rounds or they have rifled barrel. This was a ruling made by ATF some years ago!
Ok, "Anti-Personel" round is any round that was specifically made to injure or kill someone like batons, bean bags, rubber bullets/pellets, bunker busters and so on.
"Possession" - the meaning of it is very vague! Some say "in same location" and some say "in the launcher itself". I have no knowledge of ATF ever putting in writing the definition of this term. It's kind of like full auto groups and semi auto firearms. I would not personally have anti personel rounds in the same loacation as a non-registered launcher just like I would not have full auto parts in same location as a semi auto firearm.
Other rounds. Last year ATF ruled that manufacturing and sales of explosive rounds "Bird Bombs", was illegal without proper ATF explosive license. This does not only apply to 37mm but to any type of explosive round such as 15mm and 12 gauge. I am thinking it only applies to new production because you still see them for sale at gun shows. But do not quote me on that.
So what can you shoot without having to register your launcher? Smoke, flares, star burst, parachutte flares and stuff like that. I need to caution you that if any of these type rounds are used in an "anti-personel" type situation, it could deem your launcher as a destructive device and now you broke the law!
Beehive was not manufatured for the 37mm but if it was it would require the launcher to be registered. Remember firing ammo that is manufactured to fire from a registered firearm, shotgun/rifle, from a non-registered weapon, launcher, is not legal! So using the adaptors to shoot shotgun shells from your launcher would put it into the registered classification.
This is just a breif overview and by all means is not complete. Make sure you also check state and local laws because they could be different from federal requirements.
I hope this helps!