You can empty out 1l of engine oil and stick 1l of ATF in there and run it for a few hours around town at a moderate speed. It'll clean out any oil sludge and thin out the oil ready for the flush.
But the mayo in the cap and dipstick will be down to short distances. Remember engine oil operates at 90-100 degrees, and you need to run it at this temperature for a while to burn off any condensation in the oil, otherwise it'll create the mayo. Just take the car for a good blast down the motorway with the revs quite high (Italian tune up

) and that should clear it up nicely.