I wouldn't use a clipping mask here. I'd use a Layer Style.
You can apply an Overlay
Layer Style to the group

This essentially provides the same result as using a clipping mask.
If you want each layer within the group to be individually colored.
Right-click the Effects
item in the Layers panel and choose Copy Layer Style
. Then delete the style from the group.
Then highlight all the layers in the group in the Layers Panel, right-click and choose Paste Layer Style
.

You can then adjust the layer style on any individual layer to tweak any coloring specifically.

If you're dead set on using a clipping mask, you'll need to duplicate the mask for each layer, then merge the clipping mask with each associated layer. Of note, if you use the Create Layer
option when right clicking a the Layer Styles, you'll see that the overlay Layer Style actually expands to be a clipping mask on the layer (Which You'd need to merge as well to "bake in".)
Action
, but a script could get you all the way to the most ideal solution. — I was also thinking it might've been easier if you originally colored each part separately. If you needed to export multiple colors, all you'd have to do is select each color layer and hue & saturation or whatever (maybe), but that might make it more complex if you have multiple fishes.File > Automate > Batch
and an action that trims transparent whitespace... Or edit the script to trim before saving each image which would be a fairly simple change, though you would also have to undo the trim after every save.File > Scripts > Browse...
opens script and that would more or less achieve the same thing (without trimming each output image).