There should be a copy among the official inquiry papers.
Also the underwriters would need one to check off subsequent B/L claims as they came in.
And a copy should have been filed for outward clearance at the custom house at port(s) of lading/departure.
Of course with the passage of time and other contingencies none of these may have been archived or otherwise have survived.
I would think that your first line of enquiry should be the official inquiry dossier; this should give you leads to the other repositories.
A copy may have reached Liverpool, where Canadian Pacific Steamships were managed, but that's an even longer shot. The basement of the Royal Liver Building is only so big. The company is still extant as CP Ships (I think they have a web site). You could ask them if they have an appointed historian who can field such enquiries.
I do not think that a complete cargo manifest was ever found, even in the Inquiry papers, which have been found only two years ago.
The closest I can get is: 1-a stowage plan for the last voyage, which gives a general list of cargo, and 2-the insurance claims that were filed later, which give an incomplete, but accurate account of what was in the ship for her last voyage.
If you are interested, I could try and post this stuff here.