There are no oil cooler connections to seal. We detached the two oil pipes that ran from the block (by the oil filter housing) up to the cooler and back again. We replaced them with a hose that links the two outlets on the block together, so the oil just comes out of the block and back into it again.
Not really concerned about the Stat being bunged with oil. What surprised us when we removed the header tank (coolant reservoir for the pedants amongst us) was that although it was full of oil, no oil appeared to be anywhere else in the cooling system.
After fitting the bypass and running the car for about 20 mins there was a slightly oily residue in the top of the header tank, so we removed it again and cleaned it out. Upon reinstallation, no further oily residue has appeared, so I really cannot work out how so little oil managed to get circulated around the cooling system given the header tank was completely full of oil and there was oil in the valley that the oil cooler sat in. Not sure how much oil had been lost but it had been at the full mark on the dipstick when I last checked it, but was only just touching the very bottom of the dipstick after the leak was discovered. I had only done about 15 or so miles since I last checked the water and oil levels which were both normal, so it may be, as someone suggested previously, that I caught it early enough to stop it getting circulated around the cooling system.