As a followup to #529 where I asked to be able to choose an alternate browser for the "Open ..." action:
There is an app: Opener (proprietary, costs $1.99 at time of writing), which enables a "Share" item that, when tapped, pops up a list of candidate apps. This is primarily for mobile-app launching from desktop URL's, like YouTube, but you can give it your preferred browser (in my case, Chrome) as an always-available fallback option.
So I think instead of this feature request, perhaps an even more useful one would be a "Share ..." choice in the pop-up selection menu. This would enable not only opening other browsers, but opening other iOS-native apps like YouTube, Facebook, etc.
shaps80
commented
4 years ago 
As a followup to #529 where I asked to be able to choose an alternate browser for the "Open..." action:
There is an app: Opener (proprietary, costs $1.99 at time of writing), which enables a "Share" item that, when tapped, pops up a list of candidate apps. This is primarily for mobile-app launching from desktop URL's, like YouTube, but you can give it your preferred browser (in my case, Chrome) as an always-available fallback option.
So I think instead of this feature request, perhaps an even more useful one would be a "Share..." choice in the pop-up selection menu. This would enable not only opening other browsers, but opening other iOS-native apps like YouTube, Facebook, etc.