Certainly can understand you being nervous. Whenever your air is handled by the cruiseline, they have the responsibility to get you to the ship. We live on the east coast of the US, and I have not heard anything more about a strike. There has been strike talk for several months. Keep watching the boards for info on Galaxy. You may want to talk with your Travel Agent for more definitive advice.
Wishing you a trouble free foight and smooth sailing on your cruise.