Those are the operative words - fall apart. And that's exactly what cooked/canned salmon does. But I still use it for making salmon patties. However, if you're talking actual 'burgers' that you're wanting to grill and use on a sandwich, I would definitely go with raw salmon, very coarsely chopped. Then you can add your other ingredients and form them into patties.
But I'm no real expert on the salmon burger thing, so I would look up different recipes on the internet to get some ideas.
As for capers, that's a personal preference, as far as I'm concerned. I can't stand them, so I would never use them in something like that. Well, in anything.