It makes sense that the fishtrap would stop working as the blocks are no longer "water". But his produces a niche enhancement .... ice fishing. This enhancement would add the following:

Frozen Rock Fish
Frozen Clown Fish
Frozen Puffer
Frozen Salmon

Adding the "frozen" fish to a furnace will produce the normal cooked fish, but take a longer burn rate.

Ice Fishing will have its own loot table produced via a config file.

On the topic of ice fishing. It would be a "nice to have" feature to have more fish that are actually caught trough in-world ice fishing. "...cold water fish such as lake trout, herring and whitefish." [1]

These could be cold-biome limited. For bonus points it'd be stellar if there were actually fish entities for these from 1.13 onwards too. (It'd add more content to fish traps too)