I don't know that this is necessarily the best way to do things, but if it were me, I'd likely rig up something using a few disposable aluminum pans :
To assist in our cleanup, we'll start out by assuming that your fryer is set to one side of a full sheet pan, with the other side free as a catchment area for any spills while we're emptying it.
First, we make a cooling device using 1/2 deep pan filled with ice, and then another 1/2 deep pan on top of it. Squish one of the corners of the top pan to make a sort of a spout. Set this on the vacant side of the sheet pan. To reduce the possible mess from working too quickly, cover the side of fryer near the cooling container with some aluminium foil.
Next, ladle the oil from the fryer into the cooling tray. Swish around the oil 'til it's cool enough to handle, then lift the oil-filled tray out and pour into your final recepticle for disposal. How much oil you put in each time depends on how sturdy the foil pans are.
Once you get the majority of the oil out of the fryer, you should hopefully be able to move it safely. If it's still hot on the outside, you can try wiping it down (to remove any oil residue), and then wipe it with wet towels to cool it down.
If you think that would take too long, your next option would be to find a metal can that could fit inside a larger bucket and seals well. Take whatever your local equivalent is to a 5 gallon bucket, add some heat-stable insulation along the bottom (eg, mineral wool), center the metal can on the inside of the bucket, then insulate between the can & bucket. You'll want to modify the lid for the plastic bucket so that it has a hole in the top to snugly fit the funnel. Assemble the whole thing, then either ladle into it, or attempt to extract the container and pour it in directly. Remove the plastic lid, seal the can, then re-attach the plastic bucket lid (but without the funnel).
The problem with this method is that you haven't actually cooled down the oil, and with the insulation, it'll stay hot for quite some time. (slowly heating up the outer container). You'll likely want to transfer the oil back into something disposable once it's cooled down enough to handle.