Nick, just be discreet and find a relatively quiet place on the rocks etc. There was a guy sat quietly naked in front of Kumharas at Sunset recently and sparked a huge debate on one of the local groups. One view is that it's a fundamental freedom to be cherished in Ibiza. Another is that it's unacceptable exhibitionism. Personally I don't care and if I had kids I would want them to see nudity as a normal part of life not something "wrong" or "weird" to be ashamed of or associate with sexuality. Provocative £500 Italian thongs are about sex. Nudity (imho) is not.
Be extremely careful of your stuff round San An - very likely it will get nicked. I have gone skinny dipping in the Bay at night after clubbing in the past but only after making sure I wasn't seen burying my stuff and key. It was a very brief affair (so to speak lol). The reason was quite simply to stay dry on my way back.
Otherwise I get naked loads in Ibiza as do many others especially Spanish locals. It's completely normal and a lot of the "tourist" fixation with keeping swim stuff on in the sea is from cultures who sexualize nudity. There's a completely practical reason too - means you don't have to walk home in wet clothes if you're not carrying spare stuff with you. Very often away from official nudist beaches women take off their tops and all the local guys go nude. It's more conventional to head to quieter beaches to do this though. Well it is nowadays - never used to be like that, but then those were much quieter days !! My suggestion - get the bus out to Cala Conta and go be free for a few hours. It's far more pleasant than looking over your shoulder for drones and i-phone weilding weird repressed tourists in San An !