It's going to happen; a one or a few students will need to make up their exam. Good news–you have options!
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1) (most popular) make another class and just drop that one student incontact us (questhelp@austin.utexas.edu) to drop the student(s) in (we'll need your course unique and UT eids of students to be added); in this case you can release solutions as you wish, set optional timer, etc. The student would have to navigate to this other class (usually labeled make up exams or something of the ilk) and their grade would have to be transferred over (although this would also be needed for option 12), but only that one student would ever see it. Pros include students can be swapped out as needed for other make up exams (if applicable), all functionality begin retained. Cons include the student needing to navigate to this one other class. I haven't seen this be a problem in the past, but do think it worth mentioning. Please let us know if you use this option so we don't accidentally double charge students in this test make up course.
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2) the other way is to, within the same class, make a revised assignment that is set to start and stop at the same time, then grant this one student a late submit. As long as the test is kept in test mode (ie solutions are not released) other students in the class will only see the title, but not an active link (although a primer of you are not intended intending to have access to this assignment might be wanted to quell any eager students' nerves). The pros of this approach are that it's in the same class as the student is familiar with and offers it to only them. The cons are that the timeframe the student must take it in is pretty strict--ie the optional timer wouldn't be applied, it would just be the late submit deadline set, other students in the class see an assignment existing (if that matters) and solutions can not be released (en mass--we could send a solution pdf your way if helpful).
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