I just mush them up into the patties. As was said previously, they add a bit of crunch sometimes, but not really “crunch” they are almost powdery when bitten into- kind of like a soft smarties in texture- and they don’t add or change the flavor at all. If you have chunks in your patties anyway (like onions or celery or even bits of uncrumbled cracker) you don’t really notice them. And they add calcium. 
You have already gotten two good recipes, but salmon patties are like meatloaf- everyone and their Momma has a little different recipe or a little twist. Me, I just wing it as far as measurements and sometimes play with different herbs and such, and sometimes they come out better than others. Here’s what I did last night:
2 cans salmon
approx. 1 sleeve of saltines (some of them went for nibbling when I was working ;)) and some seasoned bread crumbs
2 eggs
1 med onion grated
Parsley and/or dill, salt, pepper, garlic, dash of Worcestershire sauce
Butter or Oil for frying
Crush up the crackers (either with your hands or using a rolling pin, but leaving a few bigger crumbs is nice too) in a bowl, toss in some bread crumbs, add the salmon, and onions and mush it all up (you can drain the salmon or not, if undrained you can either skip an egg or add more crumbs; I drained one can and left the other). Add the eggs and mush that all together until everything is cohesive (add more crumbs if necessary) add your dill/parsley and spices and mix well.
Start your skillet heating with a glob or two of butter or a smidge of oil (I don’t measure these things). While that’s going start forming your mush into patties- I use an ice cream scoop and then flatten it with my hands to form patties about 4 inches across, maybe an inch thick (possibly a little less). You can either roll the patties in flour or bread crumbs then fry them or do like me and just put the patties straight into the now hot skillet. When sufficiently browned on one side, flip them over but keep in mind the first side will take longer than the second. Don’t overcrowd the pan (like all things) and add more butter or oil as needed.
Yummy!
After having to buy a new transmission a week or so ago, I will be having a few more weeks of being broke, so I am looking to class-up some other cheap foods too. I have a bag of potatoes and some smoked sausage for tomorrow, and I have all the pantry staples…any ideas what I could do that will still be aesthetically pleasing enough for 4 discriminating eaters? I am thinking about some kind of skillet meal with fried potatoes, onions, and the sausage…and I can almost come up with it, but just not quite…
I do this to a can of oil-packed tuna:
Huge nice bakery roll cut in half containing layers of
tuna, boiled egg, radishes, lettuce, tomato and anchovies.
You could theoretically, croquette my very simple patty recipe by rolling the patties in flour, dipping them in an egg wash, then in aseasoned breadcrumb mixture with parsley and finely chopped dried lemon Peel. deepfry the pattie
I can’t give up the cream peas, however… that classic warm pea milk bechamel is what defines a salmon patty for me. I don’t want that fancied up… salmon patties are a very simple and basic dish. You don’t mess too much with basic-optimal.