Definitely a new chain if you’re doing it properly and for the cost of a 10sp chain vs the pain of a broken chain I would. If you don’t already know how to correctly size a chain, check the Park guide (apologies if this is egg sucking but comments about extra links make me wonder).
Derailleur cage length is important for ‘chain capacity’. For a 1x it’s almost redundant. Ability of a derailleur to cover a cassette is only accidentally to do with cage length. A GS (Medium) should be fine. The top jockey position is more important- this is what you’re adjusting with b screw, goat link, radr etc.
Every combination of frame, derailleur and cassette is different and there’s a bit of experimentation needed unfortunately. Unless you know someone with the exact combo, if money is tight I’d try without the goat link etc first and see what happens. You might be happy with it just on the b screw…