Personally it sounds like a kid that's probably not worth gaining an ulcer over. I would just make them more tired by assigning them a lengthy research paper to make up for the performance. If it's a HS kid make it 5 pages, 3 pages for a MS, with works cited, 12pt font, 1" margins, etc. Make it clear they have it due on the following Wednesday.
You now look like you're bending even though you're really making it much more worth it to attend your performance.
If I had admin support on it I would just give a zero based on it not being a medical excuse and them being at school on that day. Depends on your situation how far you can push it. (I would be backed up either way, but the research paper looks better to admin since you are giving)