I think there is some misunderstanding here...
There is no cooler in the LS radiator. The cooler for the transmission, power steering, and hydraulic fan (gen I only) is in front of the radiator and there is no way for fluid from it to mix with coolant as there is a really big air gap between the two. Look at your LS. There are no cooler connections going into the radiator.
The V8 sport does have an engine oil to water cooler, and failure of this is what the thread is talking about. The cooler is between the oil filter and the adapter to the engine. The lower radiator hose has to smaller hoses off of it that run to the cooler. If you don't want to replace the cooler, then bypassing it is as simple as removing it and changing the lower radiator hose to the one used on the non-sport (since it doesn't have the two hose connections to go to the cooler.)
The engine oil cooler (the only cooler that could mix oil with coolant if it fails):
http://deneau.info/ls/s6x~us~en~file=s6x31025.htm~gen~ref.htm
The transmission and other hydraulic cooler (no way to mix fluid and coolant):
http://deneau.info/ls/s6x~us~en~file=s6x72006.htm~gen~ref.htm