Remain in key of G. If the song was in G sharp, then you would remain in G sharp. All scales/modes relative to G will work in G but all scales/modes relative to G# will not always work in G. At a really basic level, without looking at shared notes, G# is as much different to G as F is.. or any other key.

Of course things like this are open to debate because scales/modes share notes and you might find a scale/mode that belongs, in theory, to another key that still works with the key you are actually playing in.. depending on a whole bunch of things including the style of the music.

But the simple answer is: If it's in the key of G Major, you should be playing in G Major (and all of its relative scales/modes).