I don't know what it is about Visio's Save As Web Page function that I find intriguing, but every time I spot a question about it I feel bound to dive in and take a look. The most recent question in the newsgroups asks how to change the mouse cursor when the user hovers over a shape with a hyperlink.
Although there's no way to change the this type of behaviour through the UI, there's a fairly easy fix if you're prepared to do a bit of post-publish text editing...