Can I use a single insulated wire to upgrade knob-and-tube?
No, it's not to code to run a single insulated hot wire. It's also weird and confusing.

Instead, replace as much of this as you can. If you must keep some K&amp;T, run it to a new junction box and change it over to NM-B (aka Romex) cable. Rewire these fixtures with NM-B. Looks like if you can do a new run from the attic for the switch box, you should be able to do the same for the other boxes nearby.

P.S. Removing a chimney gives you a great opportunity to change out a bunch of wiring throughout your house. Future you will likely appreciate it if you can modernize your wiring now.