Can't see the need to stir. The coiled tubing does the mixing for you. Not to be all doom and gloom, a gentle swirl to mix is probably OK. Not needed though IMO.
I wouldn't wait. I'd bottle immediately. I feel dirty disagreeing with the great J Palmer's howtobrew.
Edit: Not sure exactly what th elink says as I can't open that page at work.
I've had uneven carbonation from just letting the swirl stir in the priming sugar/water solution so I now do a gentle stir and that seems to have solved the problem. YMMV