There are a handful of words in classical Latin that denote skill in handling social situations: urbanitas, humanitas, comitas, facilitas.
Facilitas in particular might be ideal for representing being at ease in or having an easy-going manner in a given situation. However, it has a rather wide semantic field. Therefore, to specify it as a social grace, ancient authors often paired it with another word that is more recognizably social in nature. In Cicero we find in one instance comitatem et facilitatem, and in another facilitate et humanitate.
Also, lenitas denotes a gentle manner that might be considered tactful as opposed to forceful.
Dexteritas is a rather uncommon word, but Livy does use ingenii dexteritas parallel to comitas in describing Scipio. The meaning there seems to be that he was a very quick-witted or highly adaptable.