Hello Ken,
Make sure you have the correct size wrenches for the oil lines first (22mm, 27mm). Always use two wrenches to unfasten or you may damage the radiator (one to hold radiator fitting and one to unfasten oil line). The inside fitting may require a "skinnier" wrench than usual.
Removal of the battery is beneficial and safer during the job. The radiator with the oil cooler is normally removed together which involves removing the hood in most cases. Read the posts on hood removal first if you choose that route.
Some owners prefere to remove the radiator from below without disturbing the hood.
Two "carriage" like bolts hold the oil cooler to the radiator side. The nut is a 10mm.
These oil coolers are made of steel to withstand high oil pressures and prone to corrosion in salty regions and northern winters. Leakage and loss of oil can result from failure by corrosion. Normally these CANNOT be repaired by a radiator shop. They are fairly expensive to replace with new. Here again I believe many sedans of the era with these M130 engines used the same oil cooler.
During restoration these should be carefully bead blasted and re-painted to protect the steel fins and cores from corrosion.
The expensive high pressure rubber oil lines are also usually ready for replacement after twenty or thirty years also. At least check them carefully. The fittings on the ends are removable and the hoses can be rebuilt, but consider the risks involved in this.
If you have an automatic transmission replace the transmission rubber hoses going into the radiator at this time also. These are fairly inexpensive and easy to change.
Good Luck!
Joe Alexander
Blacklick, Ohio