There will be list for the allies of the major nations. The problem is do you list it as Canadian if the crew is Canadian but the ship is British. Or list it that way if they built it and man it themselves?
Most of the time the ship falls under British Leadership but is stated to be Canadian crewed. Same goes for the others. I have some ideas but would like to hear what others have to say.
It gets messier than that. There was a "New Zealand Division" of the Royal Navy until 1941, when the RNZN was formed. How would ships like HMS (Later HMNZS) Achilles be classified? In addition, much of the RAN at this point consisted of vessels transferred from the RN, often with at least part of the Officer Cadre intact. This occurred with smaller, as well as larger vessels. I've got a mate here who's father served on Flower-class corvettes on the Murmansk run, and he was on one of the ships transferred to the RAN in 1945, along with the whole crew!
Additionally, IIRC, all of the Commonwealth navies served under the overall administration of The Admiralty. My inclination would be to group these forces together, under a heading like "Royal and Dominion Navies" and identify on a ship by ship basis when needed