weapon animations and constant spell effects

Yes, any piece of equipment in the game can be made to give a character Regen while it's equipped. This is by far the simplest way to achieve what you want.

ADDITIONALLY! If you DO try to give someone Regen via events (like Shadow's Interceptor status), then either you'll have to apply it every time a major event occurs (because most events auto-matically remove all statuses except Interceptor), or you'll have to edit the code that heals all status effects so that it never removes Regen from any character. (There are actually a few different places where this occurs apart from the main command, so you'll need to be really thorough with the event dump if you go this route.)

If you don't understand what that last paragraph meant at all, then you should probably just use equipment. If you understood it a little (and all the implications it has for how the game would play), then I can walk you through the process if you need it.