I would do it when its really cloudy and maybe light showers. Or early morning or evening and then I would want a few cloudy days so It can adapt to the shock of being transplanted.
Mine are usually hardened off in 3 gallon pots and droop for like a day and come right back it's not too big of a deal. You can transplant whenever. Just not a scorching hot day.
The convention is evening as the sun, is going down the earth cools, gives time for the roots to be established for the dawn,
best time to water is 16:30 hours so plants can drink and be rested for tomorrows onslaught
I was thinking early evening myself. That gives them the cool of the night to settle in to their new home. My outdoor grows in the past have all been in containers except once when I grew some Oaxaca beans that I put straight in the ground. I got 23 out of 30 germinated and they grew to 7' and all but one was ripped off. The one I got before the rest were ripped was an early bloomer and was some of the best sativa I have ever had. Anyway, I am going to put the present girls out in the ground. I kept putting it off but now I have to and I'll only be able to visit them once a week and I'm already suffering from separation anxiety.
Here's the girls that I am putting out. They were seriously mauled by grasshoppers last week. I found some stuff by Bayer that I sprayed all around (not on the girls) and that took care of the problem.