Allowing .exe uploads (old WPSE posts no longer work)

WordPress provide a hook to change the default mime types, like your hint in the question. The follow small code source demonstrated the change to allow a exe-file.

add_filter( 'upload_mimes', 'fb_enable_extended_upload' );
function fb_enable_extended_upload ( array $mime_types = [] ) {

   $mime_types[ 'exe' ]  = 'application/exe'; 

   return $mime_types;
} 

It is not necessary to change the database entry upload_filetypes.