this seems like something best solved with a bookmarklet
let me see if i can knock one up quickly
okay, i got a bit distracted, sorry it took so long
javascript:(function() {window.location="https://duckduckgo.com/?"+window.location.toString().match(/q=.*?(\&|$)/g);})()
alternative code block
javascript:(function() {window.location="https://duckduckgo.com/?"+window.location.toString().match(/q=.*?(\&|$)/g);})()
just drag that into your bookmarks bar, then click it when you're on a google search page (please message me with any questions or bugs, i wrote this in five minutes with an online regex tester)
also, thank you for this post - i'd never thought of doing this, but it's a good idea
edit 2: okay, lemmy-ui currently has a bug with ampersands. please replace &
in the script with just an "&"