I'm going to change the transmission fluid on a '96 B-Body with a 4L60E transmission and an LT1 engine. The transmission fluid pan does not have a drain plug. I'd rather not drop the pan unless I have to. Is it safe to disconnect one of the lines going to the cooler and let the transmission pump the old fluid out in park or neutral? Is it OK to let it pump all the fluid out or do I need to be adding new fluid while the old is coming out?
I can't say for certain if it's bad. However, I would not let the transmission run dry while the pump is moving. If it's anything like the oil pump on a car engine, it will use it for lubrication of the valve bodies and hydraulic parts. It may get air in bad places as well.
However, they do make automatic transmission transfusion machines that do almost exactly what you are describing. You hook two lines up and it replaces it with new fluid.
Anyway, the service manuals specify to drop the pan to drain the ones without a drain plug.
You can replace the filter while you are in there. You can loosen one side and then remove all the bolts from the other to try and contain the mess that will ensue to one side. Then remove the rest of the bolts and attempt to drain the rest out. Watch out when you remove the filter, more fluid tends to go everywhere. If you want to do a complete fluid replacement, you'll need to take off and drain the torque converter as well.
Typing this reminds me of how much I preferred manual transmissions when I worked at a shop...