Either in the model or with on the fly binding you can create joins with non primary keys as follows
public $hasOne = array(
'RelatedModel' => array(
'className' => 'RelatedModel',
'foreignKey' => false,
'conditions' => array(
'`MainModel`.`random_field` = `RelatedModel`.`some_field`'
)
)
}
the trick is setting foreignKey to false so cake does not try anything and then setting the conditions manualy, also note that the fields are excaped and in one string as something like
'`MainModel`.`random_field`' => '`RelatedModel`.`some_field`'
would output
SELECT ..... FROM ... LEFT JOIN ... ON (`MainModel`.`random_field` = '`RelatedModel`.`some_field`')
which would try join rows that == 'RelatedModel.some_field' (the actual string)