Iris are very tough plants and can handle whatever is more convenient for you in digging them. When you're digging them up they don't have to be put back in dirt right away, but you don't want them to totally dry out (at least I think it's bad, I could be wrong!). I usually cut the leaves down a bit to reduce stress (and this helps the plant not fall over when it is replanted). I keep the roots moist but not soaking wet--I might put them in a shallow tray like you put under a pot with about half the root in water, but only for a few days so the roots sitting in the water don't get too wet and gross.
If you want to dig them more than a few days before the swap, potting them in dirt would be kindest to them. If you dig them right before the swap then just trimming the leaves shorter, keeping the roots moist, then bringing them to the swap wrapped with plastic or wet paper would be great. I think that's what I'm going to do.
JQSen, the more sun, the happier iris are. They supposedly like good drainage but plenty of moisture. Mine almost all grow at the edge of the street where they have good drainage but it is in fact quite dry. They get a lot of sun there and some plants spread medium fast, some slower than that. Yellow flag water iris spreads pretty fast I think. The purple and yellow one I'm bringing spreads medium fast. I do grow irises in shadier spots, even on the NW side of a thick maple tree, but they only bloomed there for a few years and now it's too shady for them, I need to remove the survivors before they all perish. So they can take a surprising amount of shade but if they don't bloom in 2 years or at least get bigger, it's too shady.