If you really don't want a heater or filter your best option for a five gallon is a single paradise fish. They are anabantids a lot like bettas but they are fine with cold water. They are also forgiving when it comes to water quality, but in a 5 gal without a filter you will need to be doing water changes of 50-75% a week. Paradise fish are not quite as belligerent as bettas, but in a five gallon tank you could only have one because it's not enough space to keep a male with females or two males. They are just as bad with other fish, if not worse because they will actually eat small tankmates. So if you go with a paradise fish that's all you could have.
Have you considered air driven filtration? There's no electricity/water combo there as the air pump does not contact the water. Most air pumps are only 5W or so, which is considerably less than the other appliances (computer/TV/toys) that the child would play with every day - the only danger would be if he/she pulled out the plug, and presumably that's no more likely than it is with any other electrical appliance. The air pump is usually hung on the wall above the tank, so it wouldn't be hard to put in a nail and tie the pump to it out of the child's reach, as long it was attached firmly enough so they couldn't pull it down by yanking on the airline. The pump can also be hidden in a cabinet or cupboard. The airline attaches to a bubbler in the tank - the rising air draws water through the filter media. It's not a particularly effective means of filtration but it would be fine for a small group of white clouds (6 or so), again with 50-75% weekly water changes.
You need to rehome the betta ASAP, they are absolutely not okay with cold water and he will be really suffering if the temperature is falling very low at night.
Rosy reds are rosy barbs, they grow to at least 10cm/4 inches with 15 reported so stay away from those. White clouds are your best option IMO, but if the bubbler really isn't feasible stick to paradise fish.