The 'best' method?

There are others which are quicker, easier, or don't require any special tool. But the 'best' method for removing oils from a mould is an ultrasonic cleaner.

Specifically ...
Use a 2% solution of Micro-90, and place the (disassembled) parts of the mould in a basket or rack which keeps them up off of the bottom of the tank.

Fifteen minutes will probably do the job, and have some very hot water available for a quick rinse.

The metal will be totally 'bare' and flash rust is a possibility to watch out for.
Coat the outside of the blocks with (dry) spray-on graphite or Bullplate.
Don't allow any ... or anything else ... inside the cavity.

When reassembling the mould, put anti-seize compound in the threaded holes so screws can never get stuck.
Place a tiny amount of the anti-seize under the pivot screw washer (where it rides on the block) and between the washer and the head of the screw.
That is actual lubricant for a metal-on-metal pivot point ... much better than any kind of 'wax'.

Mount the mould on the handles using anti-seize in those holes, too, and you're done.

Pour your cleaning solution into a big plastic bottle for future use.