Hmmm, G#7, maybe?
Seriously, though...you can pretty much always play an Ab in place of an Ab7 though if you are playing solo the song will lose a little of its character at that point.
Do you know your barre chord shapes for G or G7? If so, just move that up one fret. It's fairly easy fingering and I bet you could learn it by June 1.
for the barre G7...
barre the 2nd fret with the index finger
with the second finger, fret the 2nd string at 3rd fret
with the ring finger, fret the 4th string at 4th fret
with the pinky, fret the 3rd string at the fifth fret
for the G#7 (Ab7) just move the whole shape up one fret.
BTW, this is one of those cases where you don't necessarily have to have the entire chord fingered before strumming. It can actually sound a little fancier if you get the G down, then hammer on the 3rd string with the pinky as you're strumming.
It's too bad you don't need a G#Maj7 - there you could just slide the three fingers of your G up one fret. Actually, if you're playing solo you might try that and see if it sounds okay with the rest of the song (though if it's a well-known tune it's probably going to sound "wrong" to people who know it well). If you're playing with others you definitely
don't want to play a maj7 against their dominant 7...