OH MY GOD! NO! Absolutely not! That's practically cheating already! There is no way that you would be able to control your urges and, obviously, she wouldn't be in control either. Men and women can't be friends! It's all sex, all the time. I know that when I guide a raft with female clients, we always do it, right there on the river.
But on a serious note, everyone in the relationship needs to be comfortable. If your GF feels uncomfortable, it's her right to have those emotions, right? It sounds like you guys have great communication skills, so that's an awesome start.