You probably are around more germs in and around the seat and tray table than what's in the water. The water is supposed to be heated to kill whatever's in the supply for making coffee. As far as washing your hands, a small travel size bottle of hand sanitizer should take care of that.

I personally don't worry that much about it. Airplanes are full of germs and who knows what your fellow travelers may be carrying on board. I'll take the coffee over a seatmate who's sneezing and sniffling the whole trip.