Justasking, try this...
Instead of applying the minoxidil to your wet head, instead, wait until your hair has completely dried and go ahead and style it. This is a little trick that Cassin from these MB's taught me and it has revolutionalized my am minoxidil schedule.
THEN, after the styling, slip into the bathroom and take your minoxidil dropper (assuming you have a DROPPER, this won't work with a dauber) and fill the dropper with minoxidil. Then, pull the dropper from the minoxidil jar and wipe the outside of the dropper so it won't leave residue on your hair. Then, using the dropper, gently poke through your styled hair until the dropper hits your scalp, and gently let a droplet go. DON'T rub it in, just let the minoxidil sit until it is absorbed. Keep doing this, dotting your affected thinning areas with minoxidil. This method keeps the minoxidil OUT of your hair, for the most part, and you don't have to worry about drying time because the wet minoxidil will be hidden by the dry, styled hair above it.
Keep in mind that you might have to sit in the bathroom for several minutes, to make sure any excess minoxidil that drips off is wiped up so you don't have oil streaks down your forehead. But, this is in my humble opinion the best way to apply minoxidil when there is a tight turnaround time. I do this every morning and manage to get about 1 to 1.25 mls of minoxidil on my head and still be office-presentable a half hour later, even though there is still wet minoxidil on the roots. Give it a shot, practice it before your trip, and let me know if it works for you. All the best, TG