If you are going for FUE, your nervousness is really unwarranted. You will discover that it really is no big deal. Strip is another story, entirely. I have had both and there is a MAJOR difference.
For my first four strip procedures, I would fly to Chicago early in the morning, have the procedure and go directly to the airport for the flight home. This made for a long day, but it was worth it to me.
For my strip with Armani and my two FUE procedures in Toronto, I would fly in late on the night before the procedure. I had my procedures the following day and would leave in the morning on the following day. I highly recommend this if you are having any frontal work, because you will get swelling. I got home from the airport following one procedure and did NOT recognize myself in the mirror and just had to laugh. I could not imagine what the other passengers must have been thinking. If anyone asked (and they did), I just told them that I was in a car accident and that was the reason for the surgical cap and gauze. You see all kinds of strange people in an airport - you probably will not stand out all that much. I, of course, had to go through customs travelling to Canada. They never once asked me to remove my hat or asked about the surgical cap on the return flight. I was pleasantly surprised. The reason I opt for leaving as soon as possible is that it is WORLDS more comfortable sitting in MY living room than sitting in a hotel room on an uncomfortable bed. I guess it all depends on where you are most comfortable. When it comes down to it, who really gives a rat’s ass what people think of you in an airport - people that you will more than likely never see again.
Good luck with your procedure. Who is doing it and how many grafts are you getting?