Salmon patties with cream cheese?
The only thing which can hold patties together is raw protein. Other things can thicken them, but they don't glue them. Egg is the easiest source of raw protein. In theory, you can also use the gluten in flour, but in practice, you will have to make a dough with just a little salmon mixed in it, not lots of salmon with a little flour sprinkled, and this would taste very weird. Cream cheese won't help at all, because all the protein in it (which isn't much) has been cooked/curdled during the process of turning milk to cheese. 

But if you say that the only difference between the dip and the patties is cream cheese instead of eggs, why do you say that the dip is a snack and the patties are a full meal? The dip is likely to have more calories, by the way.