Is there any option of staying on Lake Union that would work for the 4th?
Yes, the Courtyard Marriott is accross the street from the lake on the south end. Nice location to see or walk closer to the fireworks, also walking distance to the re-vitalized South lake union area with lots of good bars and restaurants. You could also walk to 4 small boat rental areas (wooden boat center, 2 kayak places, and an electric boat place). As mentioned above spending time in a small boat or kayak on Lake Union is a unique experience and highly recommended.
Oops, this assumes you mean on land, not on the boat. I do not know of any on the water option in the lake for moorage, Blackjenner lives on the lake with an end of the dock berth, he might know better.
Keep in mind leaving the lake by boat after the show means going under 3 bridges and through the locks, at midnight, surrounded by 2000 of your closest drinking buddies (I am not sure if the locks are running at that time).