For an inversion or eversion type injury (Fancy terms for rolling your ankle, the most common kind of sprain), the main taping is going to be to try and prevent the same injury again. Most of the time the taping job is going to be a U shaped type stirrup configuration, pulling the tension opposite the direction of the injury and then taping around the leg in series to hold the tape tight. This is going to be more important with weight bearing, lateral direction change sports such as tennis or soccer, and becoming progressively less critical with non/slight weight bearing, linear activities such as swimming and cycling.
With swimming, it is very unlikely (unless you get really clumsy on a flip turn) that you are going to invert or evert your ankle on the wall during a push off, and the main motion is going to be plantar or dorsiflexion. (The same motion of stepping on or releasing the gas pedal in a car). It's also almost completely non weight bearing, which is an advantage.
If the action of pointing or raising your toes causes no pain, then it is probably safe for you to swim without taping your ankle. I would caution you, however, to consult with your doctor or physical therapist, as there may be other complications. As a precaution, you can tape your ankle (It takes a bit of practice to do it well on yourself) and swim, as there are water resistant tapes that you can purchase. But again, check with your PT/doc, they may say that swimming is safe to do without any support (Although just in case, I would wear the air cast on the slippery pool deck).