Coho can one hundred percent be caught on flies in the areas you're describing. Quite successfully at times. IMO, however, 95% of the time downriggers are just flat out going to be more effective. I think this is for multiple reasons but the ability to cover so much water/depth easily is the biggest factor. Ive said it many times that when it comes to saltwater Salmon fishing I strongly believe the biggest factor that determines success is simply having your offering in the presence of fish as much as possible. Downriggers are just so efficient for this.
Downriggers also don't require physical effort. Making endless casts throughout the day while fly fishing can really wear someone out throughout the day and cause a lack of confidence and motivation. This results in a lack of effort over the course of a day, which of course leads to a lack of results.
To me if someone is just wanting to maximize their freezer filling potential, and isn't hung up on fishing in any one particular way, then downriggers is the logical answer. However, if you WANT to catch coho in the sound on the fly we'll then the only way to become successful is to do it. By that I mean you can't catch coho on flies while you're trolling with downriggers. If you want to do it, the only way to get good and to get confidence is to put in the time. Back when I fished the sound all summer long I caught a lot of coho, both from the beach and from boats. I am pretty confident in my abilities to do so. However, if you took the number of fish I landed during any particular season of putting 100+ days on the water, that number would likely pale in comparison to the number of fish I would have caught had I spent the same amount of time trolling downriggers.
The only time I really spent much time guiding fly anglers for adult coho in the sound was 2019 before I went back to the ocean in September, and I learned a lot that season. Guiding fly anglers for adult coho in the north sound turned out to be some of the hardest work I've ever done and what I found is that on an average day on the water, say 10 hours of fishing time, we were only finding 4-5 legit opportunities. These were often scenarios where fish would show themselves within casting range, we would find points/rips that were obviously holding a few fish, maybe a random grab blind casting into a big rip, stuff like that. So to throw numbers at it, for the sake of this conversation, let's say that with two anglers onboard on an average day we had a total of 5 "chances". 5 potential grabs over 10 hours of fishing. Naturally two or three of those grabs will come when the angler is tired and not paying attention, one of those potential grabs will be a fish that jumps within casting range but the nearest angler was worn out and sitting down and unable to get a cast off quickly enough. One of those grabs is likely to result in a vicious trout set and a lost fish. And then maybe that last opportunity is a suicidal fish that happens to be clipped and at the end of the day 2 anglers walk off the boat with some stories of missed chances and a single hatchery coho for dinner. I experienced this very very often and often thought about it. What I kinda came away with in the end is that consistently catching coho in the sound on flies isn't rocket science, but it does require a certain amount of dedication, perseverance, ability and eventually experience, and the only way to really get to that level is to dedicate yourself to it. Two extremely dedicated and experienced anglers may encounter those same opportunities but are ready and able to take advantage of them so those same two guys walked off with 4 fish for the freezer. Only difference is the ability to capitalize on those found opportunities.
There are times when flies will out fish other methods. I've experienced those days and man are they satisfying. If you spend enough days out there focused on fly fishing you will certainly experience those days. But, the simple fact is that those scenarios are pretty rare and success in general will likely almost always be better with riggers. It's just such an efficient way to catch Salmon. If watching other boats catching fish when you're not is going to bother you, then that might give you the answer you're looking for. If success is measured by the number of outings that produce a limit of coho, and everything else is secondary, then riggers are for sure the safest bet. (And I don't mean that at all in a negative way. There is not a thing wrong with wanting to spend your time fishing in the most efficient way possible)
But, if you're determined to get proficient at catching Puget Sound coho on cast flies, just know that it can definitely be done, it kinda comes down to just how much effort you really want to put towards that end.
Kind of rambly I know lol. Just an off the top of my head suggestion, but my suggestion would be to maybe hold off on the downriggers. Maybe get yourself a decent rod/reel or two and learn to mooching, jig, and if you really get hard up troll a flat line or a diver. Jigging/mooching is a lot of fun in different ways, but one cool thing about both methods is success requires the angler to really learn and figure out how and where to find fish at various times. Trolling tends to result in a lot of just randomly driving around until a fish is hooked. Effective as hell, but not the best at teaching people the finer points of learning how to actually find Salmon. Those lessons learned while mooching or jigging lend themselves well to fly fishing as it really helps you focus on where and when you should be fishing and why. Focusing on learning those methods while keeping fly gear handy may start showing you more opportunities where you'd like to pick up the fly rod. If after a season spent dedicating towards that end you still feel like you're not catching to a satisfactory level you could then invest in dowriggers. At worst you'd have a stronger understanding of different methods and when to use them, and you'd also not be wondering in the back of your mind about other techniques.
Anyway, just some random thoughts.