Redundant Transmission Cooler?

[78SilveradoSWB]

I am tearing into replacing my water pump, which have led me to do additional stuff. I noticed there are 2 lines coming from the TH 400 transmission one going into the upper fitting on the radiator. The other line goes into a small, I guess transmission cooler mounted beneath the radiator core support which has a line connection to the lower radiator fitting location. Is this redundant? My current radiator is a HD 4 core which I thought has a radiator cooler built in. I know my new aluminium radiator that I just bought does. Can I eliminate this small one and plumb it back with both line from the transmission going into the radiator? Should I replace the transmission line from ridged to flex lines?