Personally I think its much of a muchness - the direct route to the airport from the N17 is via Claregalway, unless you feel adventurous, in which case...
From the N17 turn left onto the N63 (Turloughmore, Abbeyknockmoy, Moylough)
Follow the N63 (1 - 1.5 miles), then turn right onto the road for Cashla - can't recall the number.
Follow this road to the T-junction with R339. Turn right onto R339, heading for Carnmore Cross / Galway Airport.
Go straight through Carnmore Cross (airport on the left) and follow the road to the new roundabout at Western Motors.
I don't think you'll save any time as this series of roads is undoubtedly now used as a "rat-run".