What kind of a tour is it? Is it a small, private tour or more like RAGBRAI or Bike Virginia? With a private tour company, it's a lot easier to hitch a ride with a support vehicle, although I wouldn't necessarily count on it. Better to ask the tour company your question. If it's a bigger tour, I wouldn't use the SAG vehicle unless you have an emergency or mechanical.
As for walking up a climb and footwear, I suppose it depends on long of a climb it is. I've walked up short steep climbs in my road shoes, but I've never had to go too far in them. I don't generally have any place to stash tennis shoes. Where would you put yours?
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher