I had the problem, that Skype for Linux wouldn’t open links in Firefox but a different installed browser.
Exporting BROWSER=firefox didn’t solve the issue.
The solution was to tell xdg-mime the proper app for x-scheme-handler/http mime type:
Edit in your home directory the file ~/.local/share//applications/mimeapps.list and add:
[Default Applications]
x-scheme-handler/http=iceweasel.desktop
x-scheme-handler/https=iceweasel.desktop
x-scheme-handler/ftp=iceweasel.desktop
Now Skype opens all links in Firefox (iceweasel in Debian).