I think the stock derailleur won't work. Check out the Wolftooth Goat Link. If it, or something like it, is compatible with your derailleur you're in luck.
check the compatibility on the goat link:
https://www.wolftoothcomponents.com/collections/drivetrain-1/products/goatlink
It won't work.
a wide range 9spd cassette will require a rear derailleur that's made for wide range 9spd. since wide range cassettes didn't start showing up until 10spd, nobody really made any commercial hacks to make regular 9spd derailleurs work for wide range cassettes.
The 9spd bits are probably not much different from the 10spd in that SRAM derailleurs worked better natively with wider range cassettes than shimano ever did. There was some wiggle room because of the differences in design. You can certainly try that old M970 (or is it the m972?) derailleur on a wide range cassette if you have it already. you might get lucky with it, but back then, 9spd cassettes topped out at 11-34, so it might be a stretch.
But if you don't have the cassette, I'm not sure I'd bother with it unless you also grabbed the advent RD just in (probable) case.