I just don't want to be the smelly kid!
Honestly, the shower before class is what I jokingly call the courtesy shower, and just a rinse after class doesn't make me feel clean enough to go to bed afterwards.
Unless you work in a barn, or some other very dirty location, you can probably skip the shower before class... Five minutes in, no one will be able to tell the difference one way or another.
Remember that you will be in much closer contact with people than would be normal in just about any non-intimate situation. Your partners will appreciate it if you keep fragrances of all kinds to the absolute minimum. (Zero is ideal.)