I bring my own gear all the time and just slip in where ever it looks good. I usually research the area I'm going to ..Ahead of time to find out where the prime snorkeling spots are...But that does not keep me from jumping in other places I see along the way...
Yes, you can do it, but keep in mind most places require you wear a life jacket. Some places will rent them. IF you do book a snorkeling excursion, they do provide all the gear. Now, with all the weight restrictions when flying, sometimes, it is just not possible to include that with your luggage...
As Snoklr45 stated, do the research ahead of time. There are many places you can walk to from the pier to snorkel, such as in Grand Cayman. We will also take a bus or taxi too to a beach and DW will swim on the beach while I do some snorkeling. When on a beach park yourself near some rocks that is where the best snorkeling will be.
I never had to wear a life jacket when snorkeling on my own. Mask, snorkel & fins all lay flat in the suitcase & will not increase the weight by much.
O F C'er
Experiences over the years enabled me to have all the answers, but not necessarily corresponding with your questions.