My line is always "I'm a chauvinist, so I'm going to pay for us, but I'll arm-wrestle you for it if you really want a shot."

but as a man do I want to exercise power over a woman I have just met and I am into

Yes, you do. And so does she, most of the time (in this nonphysical and nonthreatening manner, to be perfectly clear). If she doesn't, she'll tell you, and then you can stop.