It's possible that someone might use "S&S" in a specific context, but it's not a standard abbreviation.
If you're looking for a way to shorten this phrase, you could use:
* "Swish & Swallow" (with the ampersand)
* "S&S" (in a specific context where the meaning is clear)
* "Take a swig" (a more informal way to say it)
It really depends on the situation and how you want to convey the message.