Problem:
Here's the thing. I have Firefox as my default browser. But every time I click a link in Skype chat it opens Chromium.

Solution:
Install extra/xdg-utils (in Archlinux) or whatever package has xdg-mime binary. This command creates and modifies intries in ~/.config/mimeapps.list
Then run
$  xdg-mime default firefox.desktop text/html
$  xdg-mime default firefox.desktop x-scheme-handler/http
$  xdg-mime default firefox.desktop x-scheme-handler/https

You can substitute the *desktop file to the browser of choice.
This also works for other use cases where you need to change the default application for a file type.