What's a wave cactus??! Anyway, by 'drying out a bit' she would have meant to allow a callous to heal over where the leaf broke away from the mother plant. Like letting a scab heal over if you skinned a knee, the callous will prevent any nasties from invading the plant's injury site. When you plant something in the ground the soil is full of bugs and bacteria just waiting to get a foot hold into your plants, that's also why you only repot a plant to the same level of soil it was originally planted at, same principle.
As for your leaves I'd leave them to dry a week, if you have some rooting hormone then right now dust a thin layer onto the wound end (no worries if you don't though, most cacti and succulents root very easily anyway). If the open end is already dry you could take a thin slice of tissue off to get new flesh to put the rooting hormone powder onto, or it won't stick. Then anyway (with or without powder) in a week's time pop them into some of that river sand you have so much of and leave them somewhere warm but not in direct sun. You can mist the soil with water in a week or so but don't water them like you'd water a normal plant as they've no roots, and with no roots to suck up the water they'll rot.
Good luck! Lis :)

Hi
I think by wave cactus you mean Nyctocereus anthonyanus I will see if I can find a link to photo and post it.
Regards Dave hall

Grateful thanks for suggestions. We will have a go
We had about 20ml(80pts) and I am sure things are moving already. Its actually good to have mud on the boots
Regards aussiecarmel

I have never heard of the wave cactus, but i would love to see a picture. With my succulents,if a leaf breaks off, i just lay it on some dirt, and after 1-2 weeks they sprout.