Thanks for the replies, everyone.

Perhaps it's best to say something like "I've got anxiety", "I've got some anxiety issues" or "I've got more problems with public speaking than the average person" (all of these would be understatements but it would still be the truth) or something and leave it at that?

Dreading this an awful lot and just thinking about it makes me anxious. By the way, during the seminars we will be divided into smaller groups (groups of three or so) where we will discuss the assignments for a short while. After that the groups will one by one present the question and the answer to that question. I think my professor will only tell my small group that I'm not going to participate. Not the whole class. So I'll be able to tell my group that I've got anxiety (or whatever I'll end up saying), but what about the rest of the class? I'm afraid they'll sit there and silently wonder what's wrong with me and look at me etc. Freaks me out.