Maybe late here but I agree with what others have said. Offer a better or similar seat.

Agree also on not even mentioning the $100.

One thing that irks me is when someone comes with a tear-jerker or emotional story.
No offense to the op but...the wife is afraid of flying...not my problem.
I don't need to know the details of the situation, whatever reason you may have to switch the seat is as valid as my reason to not want to give up my seat.

So, ask nicely, without a sense of entitlement and focus on the nature of the offer (similar seat switch offered, flight attendants are aware of it, etc), don't focus on your perceived entitlement to switch seats. That you want to sit next to your wife is enough reason for me to consider giving up my seat or not.