Why make photocopies? Just collect their handwritten work like you did before Webwork.
When they enter their answers into Webwork, it should only take a few minutes and you can go around to make sure no one is changing their hand written work. The deterrent will be that if they cheat you'll have collected the exams and can prove it.
The danger of people changing their answers was there even before Webwork. When and if you did pencil and paper exams, did you honestly photocopy every test before you handed it back to the students to prevent them changing their answers later and claiming it was graded wrong?