Yeah, don't tell Uhaul what you will be towing. Tell em it's a Cavalier or something small. The last Uhaul trailer I saw, you pull a couple pins and the fenders fold down for clearance. Where the vehicles tires go on the trailer it's like a channel for the tires to fit in, maybe like 2" deep. If the Blazer doesn't exactly fit in the channels you could buy a couple 2x6s from the local home store to ease the tires past the channel side rails. Or if it's just close enough, a can of WD-40 sprayed liberally down the sides of the rails should squeeze the tires past the length. Sometimes just putting 40 or 50 psi in the tires will take the "bubble" out of the bottom of the tire and give you more clearance (less width) to make it up that trailer. The front tires should be the only ones you have trouble with.
If you are traveling some distance to pick up a new Blazer with a Uhaul trailer you will need to be able to think on your feet if it doesn't quite fit. These tips should get you through.