Heat oven to 350 degrees F. In large bowl, with electric mixer on high, beat together butter and sugar until light and fluffy, about 2 minutes. Add egg, corn syrup, and vanilla, and beat 1 minute. Reduce mixer speed to low, and beat in flour and salt until combined. Divide dough in half. Shape each half into a disk.

Between two sheets of wax paper, roll one disk to 1/4-inch thickness. Remove top sheet of wax paper, invert dough onto baking sheet, and remove wax paper.

On heavy paper, trace fish template. Cut out fish-shaped cookies, 1 inch apart. Repeat with remaining dough.

Bake cookies until golden, about 15 minutes. Cool 1 minute. Transfer to wire rack, and let cool completely.

Prepare royal icing: In bowl, with electric mixer on low, beat together all ingredients until combined, reserving 3 tablespoons water. Increase speed to high, and continue beating until stiff peaks form. Add reserved 3 tablespoons water to icing to thin it to the consistency of heavy cream. Divide icing among four bowls, and tint each bowl with food coloring. Using fingertip, spread icing over cookies. Place colored candy on some fish for eyes. Let cookies dry completely. To make colored circles, dip bottle cap into icing bowls and randomly dot tops of dried cookies.