Yes you can buy soya milk in all the main supermarkets like Orphanides or Papantoniou - the nearest one to Akrotiri will be in Limassol (the Akrotiri military base is in Limassol not in Paphos).
These supermarkets have large sections devoted to health food products, though from experience in buying many helath foods such as gram flour (made from chickpeas), they are often out of stock which can be frustrating.
I tend to stockpile products they always run out of when I see them , but that's not easy to do when you're on holiday!
So my advice would still be to bring some dried powdered products with you in case you can't find what you need as they have run out of stock.
