I have to solve the opposite problem a lot of the time: when a singer is starting off with their own guitar accompaniment, if I'm to join in, what key should I try? - I usually have a pile of woodwind instruments that can handle any key between them.

You look at the fret they've capoed to. For no capo it'll be G, C, E minor or A minor. Every fret up takes that set of possibilities up another semitone, so e.g. 4th fret is B, E, G# minor or C# minor.
If the guitarist is using DADGAD tuning, it'll be the same set of possibilities but a tone higher to start with. Usually I have time to sort out what instrument I'm going to use in between them setting their capo and starting to play.

Only the most clueless singer/guitarists will use wildly exotic keys, but they're the ones that need a supporting accompaniment most often.