First lets get one thing out of the way. the bulbs you mentioned are not Paperwhites Unlike their daffodil relatives, paperwhites won't tolerate freezing temperatures, but they can be planted outdoors where winters are mild. Plant them in the fall as you would other spring-flowering bulbs. They look especially attractive in groups planted in containers or the garden. But you are from Kentucky, so perhaps your winters are mild. Mine are not.
There are tons of "outdoor" daffs out there. Hey, just ask me: I have 100,000 bulbs on my property. Some are sweet little white things, some huge bright orange, some small orange cuties. etc. And frankly, most of the names I have forgotten.
But in any event, yes you can transfer when in bloom, or as they say when the green is still on. Not sure why you will do that, but just wait for the bloom to be done then to transfer, because they will flop when you transfer them and you will loose that nice look. When we split, we wait till the bloom is done, just to enjoy the stand up it gives us. And do not forget to dead head your daffs after flowering so the seed head does not take the energy from the bulb.
