This is a tough one. Yes you can decline, however, it will be hard to do so. If it's not mandatory and there's no additional compensation, just be up front and tell them that while you're honored they selected you, you don't want to be out of the classroom more than necessary, so you'd have to decline. It should be a given that students perform better when their teacher is with them as much as possible, however, research to prove this may be necessary to show the "boss."

If your principal is a good principal and has been in the classroom, the he or she will understand that your students are the absolute most important thing to you. On the days that you are out, they are not learning anything. I think you declining for this purpose shows how professional and committed you are to your students. A good principal would totally understand that as long as you are active in your school.

I would suggest attempting to say something along the lines of "I am honored. However, being away from my students for multiple days will ultimately be a disservice to them." At that point, I can see two things that could happen. 1) you'll be off the hook. 2) They won't care and you'll still have to do it. Perhaps they may be amenable enough to reschedule to after school or only half days.

You just have to explain what is going on, and do what you feel is right