I like this approach. I think it can be simplified somewhat by using more of the Location object's capabilities, along with URLSearchParams:

if( ! document.location.search.includes("useskin=vector") ) {
let searchParams= new URLSearchParams(document.location.search);
searchParams.append('useskin', 'vector');
document.location= document.location.pathname + "?" + searchParams.toString() + document.location.hash
}