Small, thin wires at the air handler are typically used for the thermostat connection. Standard thermostat wire often has several more wires in the jacket than what you need, so its not unusual to have a couple wires cut off short and folded back. Capping should be sufficient for low voltage wires, if that is what they are.

Bruce

Further there is NO situation where "taping" makes a wire nut any more legal. If the situation would appear to require tape to work, you're not doing it right (either you've misinstalled it or you're using it somewhere where it's not allowed taped or not).