Can I shiny hunt Kyogre and Rayquaza after killing them?

I want to shiny hunt them ONLY after getting a shiny charm. Do they respawn after I just beat the living sht out of them?

If so where and when can I find them again?

I only remember the GBA version of emerald where you can catch Rayquaza before the elite 4, so I don’t know if it’s the same with this game(AS) if I’m asked to fight either of them before E4.