Sounds like that shop gave you some good advice you chose to ignore.........Replacing the cooler after a bad failure and or with very high mileage is not a bad thing to do .

They are hard to flush properly and a new trans can easily get F.U.quickly from a dirty cooler.

I would just change out the whole entire radiator , there pretty cheap for those trucks and if it,s never been changed before it,s day are numbered anyways.

I would definitely loose that check ball , you won,t notice it,s gone at all.