1st Gen Oil Cooler Questions

I have an 83 GSL with a bad motor and an 81 donor engine.  The 81's oil 
cooler is damaged, which leads to my questions:

What problems, if any, will I have if I put the 83's oil cooler assembly 
on the 81 engine?

Do I have to use the larger "coolant" radiator if I use the 83's oil 
cooler?  The original radiator from the 83 is missing -- I only have the 
smaller 81 radiator (two of them, one old & one new).


Thanks,

Bob