I'm thinking of installing an aux tranny cooler, and wondering if I should abandon the radiator'* tranny cooler or not... I'd like to abandon it, but is that the best idea? It would seem like it would help the radiator just focus on cooling the engine and not have to help with the tranny.

Well, if you run the new tranny cooler before and in series with the old one then the fluid will be cooled off before it gets to the radiatior and then cooled even more.

Does anyone know if these trannies have a bypass in them to skip the cooling lines until they are warmed up?

There is no bypass on these (4T60 and 4T65) transmissions. The cooler they run, the better. Don't worry about bypassing the radiator, just place your 2nd cooler after it in the series.