Yes bad use of wording by me, jacketed is more appropriate, as opposed to shielded, however, there are a ton of wires that would be suitable, meet UL (or other standards), and have a 600V rating. However, unless you passing near another wire and/or the case, you often don’t require jacketing at all, bare wire may be suitable (just like a PCB), as long as the wire is supported. The op is asking about internal wiring, which could be many spots. I normally recommend for those not great at soldering to invest in a stripper that is good with teflon wiring and then use teflon wiring as excessive heat not not significantly damage the jacket.
1015 is often used as it is very cheap and provides better protection and colder guaranteed temperature rating than 1569 for 277V circuits.