Is it possible to configure MediaWiki to only require a login (without password) and only check that this login exists in a LDAP database?
You could instruct everyone to register with (or register for them with) an empty password ("") (or remove the password box from the signup page and hardcode it to ""), it seems they are allowed by default ($wgMinimalPasswordLength = 0 is the default). You could probably go in and remove the password box on the logon form (or setting it to hidden might be easier) as well.