Can I get the search icon to point to a custom url?

Site URL: https://pdplondon.com/searchhere

Hi,

I'm having trouble with the in-built search not returning results well so am looking to use Google's programmable search tool instead. I've set up a custom search page to embed the Google search, but would ideally like to use the search icon in the header (rather than listing a menu item). Is there a way to change the url associated with the default search icon to point to the custom page, rather than the default /search page?

Alternatively, is there a way to change the slug of my custom page to be /search (when I tried to set it up, it says that url is reserved (for the in-built search))?

It looks like you've resolved this.