"Petting the shark" refers to giving a woman a hand-job. This is due to the fact that at most aquarium shark petting tanks, they require you to pet a shark with the first and middle finger, the same two fingers used to finger your girlfriend.
Side Note: A woman's vagina also closely resembles that of a sharks brain, doubling the connotation.
Yeah, I'm totally about to pet the shark.
Performing an unnecessary overtly dangerous act.
The breaker panel was three feet away, but the electrician pet the shark and worked with the live wires.
A small fish or A misheard lyric from hit me with your best shot by Pat benatar
Yesterday I got hit with a pet shark.