So you *must* use SSMS or you are choosing to? Without having yor local machine connect (prior) to that domain, am not sure you'll be able to do this. i.e. for you to be able to right click and select 'Run As' (different user) trying to enter that user account, without having previously pulled a usr profile while connecting to the domain - doubt this will work.
If the requirement is simply to query the cube, then you could use excel. from memory, you can create a connection and supply credentials (be aware, quite possibly stored in clear text in that conxn file) and then connect using excel pivot tables.
another alternative, for them to expose the cube/s via the msdatapmp.dll (using IIS) thereby allowing you http access (again, likely using excel or whatever client tool bu not SSMS).