Combine squash and water to cover in a Dutch oven; bring to boil, and cook for 15 minutes or until tender. Drain and let cool. Scoop out pulp, keeping shells intact; reserve pulp.
Peel shrimp, and devein, if desired; chop shrimp.
Melt butter in Dutch oven over medium heat; add ham and 1 onion, and cook 3 to 4 minutes or until onion is tender. Stir in shrimp and squash pulp. Add green onions and next 4 ingredients; cook 20 to 30 minutes. Stir in 1 cup breadcrumbs. Spoon mixture into shells.
Stir together remaining 1/4 cup breadcrumbs and paprika; sprinkle over shells. Bake at 375° for 15 minutes.