If you have a spare (assuming you don't have to deflate it to get it to fit in your fender well) why do you need a tire pump? If your luck with tires is so bad that the second one goes flat before you are able to have the first one repaired you probably need new tires.
I actually carry a hand pump that was made in the USA from of all places Walmart... It's not easy but I can get air into a front tire while on the car...
"Slow anyone down with a problem", these folks will be wanting to help make repairs for you before you can get out of the car. Don't worry about breakdowns, enjoy the tour. Someone will have what you need if you don't have it. In dire cases they will get help from a local model A'er around Glen Rose.