Hey, are you the same Giddy1 from the Due in June 2005 thread? If so, how the heck are you?!?!? (Uwila here, by the way)
I'm afraid I don't think this man deserves the benefit of any doubt. He knows full well what he is saying. He wants to pay you cash in hand and he wants not to take on any employer responsibilities. He picked up on the "net" very quickly. And he knows full well what it meant.
You could, however, offer to provide these services in your own home (if you want to). Then, it's perfectly realistic for him to pay you cash. However, he should still expect to pay you when he doesn't show up (i.e. his holidays, if the child is sick, etc.)
My current but soon departing nanny has an arrangement like this. She is our full time live in nanny. A while ago I told her I didn't mind if she wanted to pick up more work in the form of a share so long as it didn't impact the care given to my kids. She now looks after another child in my DD's class and a younger sybling. The other family pays her in cash and only when they need her. They cancel at the last minute. They take loads of holiday. And so on. So my nanny does not have the level of income she expected from this family. And she isn't very happy about it. I wouldn't take this on if I were you. You could end up in a position of them expecting you to be avaibale but then not wanting to pay you if they don't show.