Are you sure mobile browsers are good at viewing desktop-aimed content?
I'm considering auto-resizing (fluid) for simple content like cssgrid.net because some placements will break or look weird. Would this be a problem for mobile browsers?
Quite. Mobile Webkit-based browsers were a joy to use long before we had responsive design. I'm not saying responsive design is a bad thing, though I'm not on the bandwagon because mobile browsers handle most websites with aplomb.
OnSwipe is definitely not responsive design -- it's changing the behavior of a site for specific a devices which already have wonderful natural web UX interactions.
Build a clean and fast site. You'll be fine.