Final answer:
Ethyl Chloride is the anesthesia from the given options that can be administered topically at TAUC, functioning by cooling the skin to provide immediate pain relief.
Step-by-step explanation:
The type of anesthesia that can be administered topically at TAUC is Ethyl Chloride. This anesthetic is used externally and works by cooling the skin rapidly to numb the area, making it insensitive to pain. It contrasts with injected anesthetics like 0.5% Sensorcaine and 1% Lidocaine, or 1% Lidocaine with Epi, which are not meant for topical application.
Ethyl Chloride is particularly beneficial in situations where a quick local anesthetic effect is required without the need for injection. As it evaporates quickly upon application, it induces a temporary local anesthetic effect by cooling the skin which provides immediate pain relief for minor procedures or as an initial step before injection of other anesthetics.