A phrase often used by servicemen to describe activities that are a bit cheeky, or morally dubious. All very hush-hush.
Beloved by Walter Mittys, sneaky-beaky stuff can refer variously to covert operations, or things that the military would rather keep below the radar. Submariners often profess to be doing some sneaky-beaky stuff, and they're often correct. Special Forces are generally a bit sneaky too for obvious reasons.
To ascertain whether someone is pulling your chain, ask a few pointed questions, and if the answer is solely 'I can't tell you that', then the speaker is probably a walt. If it was so sneaky, he probably wouldn't (and shouldn't) have mentioned it anyway.
Rumours of a special masonic-style handshake to differentiate between those who partake in sneaky-beaky ops and those who don't are utter bollocks. Those involved in such operations are also referred to as Secret Squirrels or Undercover Elephants.