Is it possible that there is a rock big and fast enough to divert Cassini someplace undesirable, such as leaving a streak through a ring, crashing into a moon, or perturbing something else from its natural state?
Cassini is very small, compared to pretty much everything around Saturn. So, no. You could drop a billion Cassini spacecrafts into the rings without perturbing anything.
I don't mean that Cassini will shift a moon from its orbit, but the introduction of foreign materials, for example, could change things.
Perhaps I'm putting too much emphasis on the naturally pristine state of things around Saturn, but I've read that also is a priority of researchers, at least in some circumstances.