I know of no OS setting that would disable tooltips within an application.
Unless you can persuade L&L to either give you a config switch or expose the API so you can write your own plugin to do this, your only option is going to be a hex editor, assuming you can find and selectively disable the code controlling the tooltips.
Anyway, here’s how to turn them off in the OS, but it’s not going to affect Scrivener.
There’s also this thread on themes. If you changed the tooltip to white text on white background with a white border (or whatever the background color of your theme happens to be), the tooltip still pops up but you’ll be unable to see it. It will, however, hide anything underneath it until you mouse away from it.