It’s an interesting thought. Although my preference would be that Kee somehow be prevented from inserting the extraneous icons in the first place, this might be an option. Perhaps instead of on/off functionality, it could be more of a “pause,” wherein the icons are removed until you leave the site or close the tab.
There was some further discussion of this issue here.
FWIW, for my ASUS router, my KeePass entry contains the the full login entry (http://192.168.1.1/Main_Login.asp) and under the Kee | URLs tab I’ve set the minimum URL accuracy to “Exact,” which prevents Kee from affecting other pages in the router configuration.