Even with Chrome set as default, and DuckDuckGo as Chrome's default engine, Finder uses Safari

Even with Chrome set as the default browser in Mojave, and with DuckDuckGo set as Chrome's default search engine, Finder still insists on searching with Safari. I'm referring specifically to the "Search With..." item that appears just below "Look Up" in the contextual menu, as when right-clicking a word in a text document.

There appears to be no way of changing which browser Finder chooses when searching from within the contextual menu. I have made DuckDuckGo Safari's default search engine as well, so when Safari opens against my will, at least it uses the right engine.

There appears to be no way to change this behavior short of uninstalling Safari, which I'd rather not do. Every help topic I find addresses only how to switch the basic defaults as described above. I suspect most people don't ever notice the remaining problem, or they just give up like I did for about a decade. I've had this problem for years, so it's not Mojave specific, but I'm now finally to the point of pulling my hair out. Also, I'm fairly certain the same issue persists within iOS, so hopefully the solution (if there is one) can be similarly applied.