But wait. There is a way. Apparently Confluence has a plugin that can use IE native Visio rendering functionality to display Visio. And apparently there is a fantastic plugin for Chrome: "IE Tab".
The two most popular ones are here (source of the discovery here):
I've installed both to try them out. Be warned, I don't know which one steals more of your private data, so as they say in the blogosphere: "YMMV".