I write it as a note for me and if it can helps some other people, it’s fine.
To change the program used by xdg-open for opening some kind of file, it’s not that hard.
First, check the type of the file:
$ xdg-mime query filetype file.pdf application/pdf
Then, choose the right tool for handling this type:
$ xdg-mime default mupdf.desktop application/pdf
Honestly, having firefox opening PDF files with GIMP IS NOT FUN.