The big challenge is that you didn't buy the tires from them. Many places won't mount tires they don't sell, and the few that do aren't as motivated to be all that helpful.
I very much don't have a fear of heights. As a kid I used to do a fair bit of rock climbing, and worked as a lighting and sound tech for a while...I've spent a lot of time way up in the air. The only real treacherous part was the getting back onto the ladder after doing the work.
Went up on my roof and re-attached a 10 ft piece of flashing that had been blown down in the wind storm we had last week. It was a little unnerving, because it was JUST too tall to use my ladder, but I did it anyway. Didn't even fall off or break any bones.