I always transfer when I watered 2 days ago so the soil is kinda moist, and I always do it when the lights go off. Think about when you transplant at full sun, they wilt once they're in but if you do it an evening before or when it's cool the plant seems ti do better. Don't take it as a fact just my observation.
About giving them a big drink... meh... idk. When I transplant I try to moisten the soil it's going in and that the seedling's dirt is kinda moist, I just have to water very little just around the stem to get the seedling to settle. I hardly ever have problems with shock when I transplant.
Good luck.
,Vegas