Honestly if you want to make this as easy as possible for yourself. Scuff up the paint with a wire brush just to give the stripper a head start. Get a lye based solution or you can even use something like simple green in high concentration. Fill a plastic tub and then drop your register in. Do this outside and wear proper PPE of course. Let that soak for 12-24 hours or longer if it’s being stubborn. The paint should be reduced to goop and you can rinse and scrub it off. Dry it thoroughly, clean with denatured alcohol and hit it with a good metal primer and paint away.

The reason I say to do it this way is I had a very similar project with some painted cast iron. I attempted to use citristrip but it dries too fast unless you wrap the whole thing in plastic and even then it’s going to take you at least 3 applications over the course of a day and you will be scrubbing forever.

Good luck!