Any way to convert a page of type X into page of type Y? I inserted a webform on a Basic Page. Now, I decided I should have created a dedicated content type to hold that webform.

So now - is there an easy, non-risky way to "migrate" that page to a new content type without the need to recreate it?

I would like to save myself a couple of moments redefining the webform from scratch, but if the db dependencies are too complex, I would rather take that cost rather than risk screwing up the db.
The Node Convert module allows you to convert individual nodes (it adds a convert tab to the node) and bulk convert. It also handles moving over values in CCK fields from one node type to another.