By all means, as long as he is not only open to the idea of it, but that he is comfortable with it, and understands how the ceremony works, what the ceremony involves, what it will be like and so on. In my opinion for someone to take part in a handfasting that isn't Wiccan or Pagan, I would suggest that he or she (your fiance in this case) should either talk with the priestess or priest that you would like to do the ceremony before hand, so they can discuss everything and get an idea of how it will suit them, if it's something their interested in and are willing to do and so on. I also suggest that you get online, such as google, and look for public handfasting ceremony videos so you can show him, so he can see what they are like, and get a forehand head start, before you guys proceed with any ceremony.
I love handfastings, they make me so happy and hopeful :)
Blessings and I hope this helps,