I don't see any warnings on their site about certain ammo (wouldn't be bullet weight but PSI) being prohibited. I assume the gun is made for "full-power" 44mag loads as I see no indication otherwise. As such, any ammo that will fit and function in the gun should be fine.
I would inquire in the owner's manual or by emailing Henry if the manual isn't available, just to be sure but I'd be surprised if there were any issues. Seems like a lawsuit waiting to happen, to make a gun chambered in a cartridge and make it so it can't handle standard ammo in that cartridge.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.