In a small bowl, stir together 1½ tablespoons water and gelatin. Let sit until gelatin dissolves.
Remove and discard trout skin. Using a fork, flake trout into pieces.
In the work bowl of a food processor, pulse together trout, gelatin mixture, sour cream, horseradish, dill, lemon zest, whipping cream, and pepper until combined. Transfer trout mousse to a container and refrigerate until cold and firm, at least 6 hours.
Preheat oven to 350°. Line a rimmed baking sheet with parchment paper.
Using a serrated bread knife, trim and discard crusts from bread slices. Cut bread slices into 24 (2½×1-inch) rectangles. Place bread rectangles onto prepared baking sheet.
Bake until firm and crisp, 7 to 10 minutes. Let cool completely.
Place 3 radish slices on each of 12 bread rectangles, overlapping slices.
Transfer cold salmon mousse to a piping bag fitted with a large open-star tip (Wilton#1M). Pipe mousse in a scrolled shell pattern on top of radish layer.
Cover each with a remaining bread rectangle. Serve within 1 hour.
Notes
*We used a Kyocera adjustable mandoline.
Recipe by TeaTime Magazine at https://teatimemagazine.com/trout-mousse-and-radish-sandwiches-recipe/