My preference is to get rid of the radiator oil cooler all together to reduce the total heat load on the engine cooling system.
When off load, the oil passing through the radiator can also reduce the avaliable thermal capacity of the oil cooler for the transmission, as you are effectively using it as a heat exchanger for the engine cooling system. (Which should be up to scratch to not need the oil cooler to help it cool down).
The number one killer of transmissions is heat, my philosohy is to keep them as cool as possible, especially on slow moving vehicles. They need all the help they can get with their inherant lack of free airflow.
In the cars I have built, we have found that it is beneficial to have the transmission cooling system seperate to the engine cooling system for this reason. The Trans-Am Firebird we built benefited greatly with two big trans coolers in place of the radiator oil cooler, we not only saw much cooler trans temps (the box was built to handle up to 700Hp) but also saw cooler temps from the worked 351 Chev we squeezed into the engine bay.
In Australia, most of the time the climate will allow the box to heat up quickly enough anyway. On my supercharged Levin import (and the N/A race car), the manual gearbox doesn't have a thermostat on the oil cooler and it has no dramas with spinning the synchros up quick enough when cold.
Just my opinion anyway...