Get to swinging your wrist and never stop!!! If you miss a chord, or just take a while for the chord change DO NOT stop strumming or slow down to accommodate your slower left hand. Just mute the strings and keep on strumming. You may not always get your chords out on beat, but the percussive chunk will drive the song along. A second method would be to start changing chords BEFORE the next measure so you can nail the chord on the measure. But whatever you do, keep your wrist going all the time at the same speed.

I used to just not play while changing chords, but I'd come back off beat sometimes. This way, you're never off beat. If you stop moving your wrist while playing rhythm it's hell to get it back to speed. You're bound to lose a couple milliseconds here and there, and that's ok sometimes, but if you screw up often enough, the audience will begin to tell.