If you have to sit down and deeply think about a question like fizzbuzz then as an interviewer I'd be a bit concerned - this is a quick check to make sure you're basically competent, not architecture of a critical piece of infrastructure.
If you just don't like hand writing and prefer typing, then that's cool with me and you can just do that during the interview (the content of interview is important, not the medium you write with).
If you're mentoring a 25 year old you'll have to prove yourself to them every day.