I do not believe there is any such prohibition. Nevelot cause ritiual
impurity in terms of sacrifices. We are all in the catagory of tumat met --
impurity from contact with a corpse, there is no altar, so carrying the
carcass of a dead nonkosher beast is irrelevant.
Similarly, touching the remains of the eight (there are only eight)
shiratzim [disgusting animals].
Miniature shrimp, snail eggs, etc, that are in tropical fish food? Don't
worry about them.
(In this and any questions of halachah, best to consult a qualified rav
that you follow!)