Peel and devein shrimp; reserve shells. Rinse and drain shells; place in a Dutch oven. Add chicken broth. Bring to a boil; reduce heat, and simmer, uncovered, 10 minutes. Strain broth mixture through a sieve over a bowl; discard solids. Return broth to pan.
Stir together bok choy and next 4 ingredients. Working with 1 wrapper at a time (cover remaining wrappers with a damp towel to keep them from drying), 1 tablespoon of bok choy mixture into center of each wrapper. Moisten edges of wrapper with water; bring 2 opposite corners to center, pinching points to seal. Bring remaining 2 corners to center, pinching points to seal. Pinch 4 edges together to seal.spoon about
Add shrimp, snow peas, and mushrooms to pan; bring to a boil. Reduce heat to simmer; gently drop dumplings into pan, 2 at a time. Cook 3 to 4 minutes, or until dumplings are done.
Gently ladle soup into bowls; sprinkle with green onions.