Your intuition is incorrect. Select was used as a verb long before computers existed, let alone GUIs. It's possible that young people now associate it primarily with computers, but I have no insights into that. Certainly all native speakers regardless of age understand that it can describe the action of choosing one class from a list of several.
Select is of Latin origin. Choose is of Germanic origin. English often contains options of different origin, and you have discovered a pair.
Sign up also fits this context because enrolling in a class will create a textual record. But signing up does not require that a choice be made between two classes. You might easily sign up for a class when it is the only class available.
Overall, any of the three would sound natural regarding enrollment in a class. Select sounds a little more formal to my ears, as is often the case with words of Latin origin. But that might not be true for everyone.