Melt butter in a pot over medium heat. Add onion, celery, and carrot; season with salt and cook, stirring occasionally, until soft, about 6 minutes. Add potatoes, broth, and 2 cups water; bring to a boil, then reduce heat to medium and simmer, partially covered, until potatoes are tender, about 10 minutes. Add corn and zucchini; simmer, stirring occasionally, until just tender, 5 to 7 minutes. Remove from heat; stir in cream and fish. Season with pepper and serve with oyster crackers.