You shouldn't do anything you don't want to. Kinda sucks for the guy because that promise could be misconstrued as you stringing him along instead of what it really was, you trying to let him down easy.

IMO, skipp the middleman, talk to the guy and explain how uncomfortable you feel, and that you were just trying not to be rude. If he has a bit of decency, I bet he would understand and tell the mutual friend the date was OK, but you guys were not as compatible as originally thought.

Or take the confrontational route and tell them both to stop pressing you into dating when you really don't feel drawn to doing it.

Your rights and emotional safety are important, and due to your trauma, it is best not to rush into things, but work them preferably with a therapist, until you feel better.