right click menu – select search

Is there any way to customise the right click mouse menu that pops up over a highlighted word or phrase?

I normally use Firefox, occasionally Safari or Brave. Normally DuckDuckGo to search, occasionally Google.

But if I highlight something, for example in an iMessage, and right click I’ll always get “Search Google for ….” if search is set to Google in Safari. Or “Search DuckDuckGo for …. ” if that’s how Safari is set.

So at the very least I’d like two options available – for two different search engines as in “Search Google for ….”/”Search DuckDuckGo for …. “.

Valhalla would be the ability to select the browser too.

Is it possible?