Cloudy cooler weather is the ideal time to harden them off outside and in such cases you can practically leave them out without shade the entire day long, with minimal moving them around after a day or two. Some people, myself included, don't even harden them if there will be a few cooler cloudy days outside, BUT this is after they were growing under fairly bright grow lights inside so the change isn't "as" dramatic... so long as there isn't high wind, it is not a good idea to put young plants without established roots in their larger container, out in strong wind, although staking and tying them to it helps...
I put stakes in at time of final transplant, windy or not. In this area they're going to need them and waiting just means disturbing roots later instead of putting the stake in earlier where there aren't any roots yet.
