I've done some renovation work on old buildings. I recommend removing ALL of the old wire. There's nothing like looking at a shabby old wire and wondering if it is hot or not. Even worse, sometimes an idiot will try to reconnect that old wire, yes, I've seen them try it.
Oh, it's on the list, trust me. I've got fossil infrastructure in here over a hundred years old - in a way I feel like I should get some archaeologists in to catalog it before I get it all out.
The scary thing is that the basement lights are still on the old wiring - roughly 1920's vintage. Fortunately, no gaslights left, although I do have one fitting in the upstairs sitting room!
Rip all of it out.