Probably used the old TIE from the death star.
But why did the wings come off? They were fine from Kef Bir to Exegol, and theoretically to Tatooine as well. Did the old lady attack his ship?
One would assume that it couldn’t withstand another flight?
But it did, it make it from Exegol to Tatooine before falling apart… TIE fighters don’t really fly without the wings, for him to be there it had to have flown there.