If your compass doesn't come in time: At least in AZ you can usually count on the sun. Before you start, borrow a compass and get a real good idea of the direction of the sun and shadows. It's not going to change much over the hour or so you're on the course and you can use that as a pretty good guide. If you know a bit about the direction of the sun's movement, you can project how the angle will change over the course of a longer event.
Yeah, it won't be too much of a big deal. For some reason, I just feel more confident with a compass. Even though I hardly ever use one. :)