I can't find the contract to see what arbitral body is provided for. (The TWU website is difficult to access right now.) Generally that body accredits arbitrators, and will provide both parties a list from which an equal number of names may be stricken by each.
ETA: I think it's the AAA, they've negotiated with them before.
ETA2: the AAA's rules on labor negotiation arbitrator selection:
12. Appointment from Panel
If the parties have not appointed an arbitrator and have not provided any other method of appointment, the arbitrator shall be appointed in the following manner: immediately after the filing of the demand or submission, the AAA shall submit simultaneously to each party an identical list of names of persons chosen from the Panel of Labor Arbitrators. Each party shall have ten days from the mailing date in which to strike any name to which it objects, number the remaining names to indicate the order of preference, and return the list to the AAA.
If a party does not return the list within the time specified, all persons named therein shall be deemed acceptable.
From among the persons who have been approved on both lists, and in accordance with the designated order of mutual preference, the AAA shall invite the acceptance of an arbitrator to serve. If the parties fail to agree upon any of the persons named, if those named decline or are unable to act, or if for any other reason the appointment cannot be made from the submitted lists, the administrator shall have the power to make the appointment from among other members of the panel without the submission of any additional list.