I'd suggest reading TPWD rules. Possession and Transport
Here are some excerpts;
Live fish, including personally caught live bait, cannot be transported from the water body where the fish were caught in or aboard a vessel in water from the water body where the fish were caught.
Persons leaving or approaching public fresh water are required to drain all water from their vessels
and on-board receptacles (includes live wells, bilges, motors and any other receptacles or water-intake systems coming into contact with public waters).
Possess or transport any exotic aquatic plant or animal listed as harmful or potentially harmful. This includes: plants such as hydrilla, water hyacinth, and giant salvinia; fishes such as tilapia
and Asian carps (grass, silver, and bighead carp);
So it's specifically prohibited to transport or possess live Tilapia and the regulations say "all water". I'm sure tap water counts in "all"
Also it's my understanding that if the shad come from a lake with zebra mussels they could be contaminated with zebra mussel eggs or veligers. So you'd have to treat the shad with bleach or other chemicals to make sure you aren't transporting zebra muscles. The live shad I've had experience with will die if you look at them wrong so I don't imagine they'll survive a soak in Clorox.
Unless I had something in writing from a high up guy @ TPWD or a permit, I would not try to move shad from one lake to another thinking it was legal.