You could put this in a button and inject it into the google page with a user script extension right?

yes, probably. but i wouldn't know how, i don't really use userscripts; i prefer to trigger things manually

if anyone else wants to do this: i release the above code under cc0, any person may use it for any purpose without let or hindrance, yada yada

That might get closer to what OP wants

i guess..? but i'm not sure of the functional difference between a button in the bookmarks bar, and a button on the page