I have a 1-1/4" pool vacuum hose I use to vacuum my pool with. The outside diameter of the cuffs on the ends are just the right size to fit inside the original (small) adapter for the over-the-wall skimmer.

I remove the skimmer hose, and just "plug in" the end of the vacuum hose, after filling it with water. Hint: you can fill your vacuum hose by holding one end over the return jet to blow the air out of the hose.