I use bleach all the time to clean aquarium equipment (saltwater tanks with corals and freshwater tanks with plants, and of course both have fish and I even have marine snails in the saltwater tank). I use a 20:1 ratio of water:bleach and rinse very thoroughly with fresh water and a dechlorinater made for aquariums (Seachem Prime) and have never had any issues with any livestock the past 4 years.
For a live well using bleach water, a thourough rinse half a dozen times and enough time for the rinse water to evaporate and I don’t believe you would have any problems whatsoever. With a proper rinse, you could use a wide variety of cleaning mediums from Ajax to dawn dish soap. Just rinse very very well and leave zero residue behind.
A strong hydrogen peroxide could work well too. It turns to water after a day or so anyways after being diluted with water.