The MIME type xdg-open uses for URIs is x-scheme-handler/<scheme>, in your case x-scheme-handler/http and x-scheme-handler/https. You can put an entry for those using your desired .desktop file in your ${XDG_CONFIG_HOME:-$HOME/.config}/mimeapps.list
${XDG_CONFIG_HOME:-$HOME/.config}/mimeapps.list
file.
 
                