lord of the rings - What did Sauron mean when he "talked" to Pippin?

When Pippin... um... 'borrows' the Palantir taken from Orthanc, he hears (for lack of a better word) Sauron say the following in his head:

Tell Saruman that this dainty is not for him. I will send for it at once. Do you understand? Say just that!

And when Pippin is shaken out of the trance-like stupor caused by the Palantir, he says:

It is not for you, Saruman! I will send for it at once. Do you understand? Say just that!

This puzzled me a bit, but Gandalf's analysis cleared up a few issues. I understand now that Sauron thought Saruman had captured Pippin, and was forcing the hobbit to use the Palantir; and it was always pretty obvious that Sauron assumed Pippin had the Ring. It hadn't occurred to me that Sauron knew nothing of Saruman's twin defeats at Helm's Deep and Isengard, but Gandalf's exposition made that clear as well.

I think I have figured out some of the other parts of this passage that confused me at first. For instance, Sauron gave Pippin a message for Saruman, obviously, but for a moment I was perplexed by the message that Pippin actually delivered. Then I guessed that Pippin repeated more of Sauron's instructions than he was supposed to - correct me if I'm wrong, but Sauron didn't want Pippin to say the "Do you understand? Say just that!" part. Sauron wanted Pippin to say "It is not for you, Saruman! I will send for it at once." Then Sauron tried to make sure Pippin knew what he was supposed to say, so Sauron asked Pippin "Do you understand? Say just that!" Pippin is kind of dumb, so he parroted everything Sauron had told him (a bit like the oath-taking scene in Animal House, where the frat president says "Repeat after me: 'I - state your name'" and the pledges say "I - state your name").

And I always figured that Sauron assumed that the hobbit in the Palantir was the hobbit with the Ring, of course, but I am curious as to what Sauron was referring to when he said "This dainty". At first, I had a brain fart and thought the "dainty" was the Palantir, then I kicked myself for being stupid and thought more sensibly.

But I am still torn between two possibilities as to what the "dainty" is: It could be (and I tend to think it probably is) the Ring itself, which Sauron assumes is in Pippin's possession. However, the "dainty" could be Pippin himself. "Dainty", in modern parlance, means something like "petite/small/delicate thing", which aptly describes both the Ring and the hobbit.

Since Sauron thinks Pippin has the Ring, and he doesn't want Saruman to fiddle with it, and he wants both Pippin AND the Ring, it doesn't really matter which Sauron is referring to as "this dainty" - he's planning on taking both of them anyway. But I'm still curious - was the "dainty" Pippin, or was the "dainty" the Ring?

And again - correct me if I am wrong in assuming that Pippin repeated more of Sauron's statement than he was supposed to.