If you haven’t been paddling with the dog yet, go some place where you can rent first to make sure the dog is amenable to this. Not all are. A 55 pound dog that is nervous on the water could cause you serious troubles. Best to find this out on a $40 rental situation in a protected area rather than a $1000+ purchase.
Going bask to basics, you may want to read an article available online at California Kayaker Magazine - South West's source for paddlesports information (Issue #10, page 6 of PDF version) - the article on basic types of kayaks. Talks about categories (such as recreational, sea kayak, sit on top, etc.), along with short summary of pros and cons.
Match that with a page borrowed from the Basic Illustrated Sea Kayaking book that talks about the ACA level categorization of flat water and what type of kayak would be appropriate.
Puget Sound is regularly Level III-IV water, so really should only be paddle in a sit on top or sea kayak. Except for wind, Lake Union would be level II at most.
The dog can’t be sitting on your lap, or you won’t be able to paddle. Needs to be a bit away from you. So for sit ins, you either need a second cockpit or a very large (as in recreational class kayak) cockpit. Maybe it could work to have the dog sit in the front seat of a double sea kayak, and that could be seaworthy enough vessel for Puget Sound. But you really would want to make sure you know how to rescue yourself in it, and even after rescuing yourself, you may not be able to bring the dog back into the kayak after a flip.
Given that fitting a 55 pound dog into a sea kayak is challenging (unless it is willing to sit in the front seat of a double), the sit on top likely is the better choice. Or, as Celia said, skip Puget Sound paddling and stick to Lake Union and protected bodies of water smaller than that.
As stated, canoes are good for dogs, but they don’t like windy areas and really shouldn’t be out in the potential waves of Puget Sound either.
SUPs do well with dogs, so that may be an option.
Note (The OPs dog is probably too big for this, so this note is more for future people who find this thread using a search) - it isn’t that uncommon to see someone open a hatch and leave it with the cover off and make that a place for a smaller dog to sit. Keep in mind that doing so takes away the flotation benefit of that hatch, so if you do flip, your may now not have enough flotation for a deep water recovery. Filling the rest of the hatch with float bags or other flotation could help reduce this issue.