For mutually exclusive values use post meta. It is faster to read than assigned taxonomies too.
It is possible to create your own interface:
- Set the parameter
show_ui
tofalse
when you register the taxonomy. - Register a meta box where you print out all existing taxons with radio boxes.
- Add a save action to assign the value to the taxonomy.
But in most cases you’re doing something wrong and misuse the taxonomy. 😉