Thanks to Visio’s Mark Nelson for the following tip:
You can add the User.visEquivTitle cell to your shape and provide a string that will display as a tooltip in the web output. The shape must also have at least one custom property for the tooltip to be visible.
1) Select the shape in your drawing that you want to add a web tooltip for
2) Go to Window > Show Shapesheet
3) Go to Insert > Section, check User-defined cells and click OK
4) In the newly created section, click on the row name User.Row_1 to select the title of the row
5) Type visEquivTitle and press Enter – you should now see User.visEquivTitle for the row
6) In the Value cell of that row, enter the text you want to display surrounded by quotes (e.g. “Hello World”)
7) If you instead want to display the same tooltip as the Shape ScreenTip enter =Comment (no quotes)
8) Go to Insert > Section, check Custom properties and click OK
9) You can fill in the custom property Label and Value if you want this information to be visible
10) If you don’t want the custom property to be visible, enter TRUE in the Invisible cell
11) Close the Shapesheet window and repeat for any other shape you like
12) Choose File > Save as Web Page to create the HTML output
As you can see this is a bit involved. The capability was designed more as a developer feature than an end user feature. I recommend tying the Shape ScreenTip to the User cell so that you see the same tooltip in both Visio and the web output. It should also be possible to use Macro Recorder to automate these steps. If your shape has a custom property but does not have the User.visEquivTitle cell, Visio will display the shape’s text in a tooltip instead.