Sue,
I am not a swimmer either (okay...I do a mean doggy-paddle!!) and I've done the snorkeling and the parasail. Here's my take on both.
Snorkeling: No, you don't have anything to hold on to when you get tired, but there is a beginner "trail" and an advanced "trail." You can try the beginner trail and if you feel more confident, then try the advanced. You do have a life jacket and it's really cool... it's flat, but you can inflate it if you want to...the first time I had the sucker blown up...then as I became more comfortable, I'd let alittle of the air out. I stopped several times and "just floated."
At one point I got water in my mask and my contacts were bothering me, so I paddled over to one of the life guards and asked if I could wipe my eyes on their towel... he was a little reluctant, but I guess I looked really desperate (and not too germy). A quick wipe and I was off again! And after drinking a Konk Kooler, I was fully confident that I could swim to Cuba!
Parasailing: You are wearing a life preserver and are securely harnessed. I started out being scared to pieces, but by my turn, I was excited!! Once I started up, a sense of peace came over me. It was so beautiful, quiet, and awesome!!! Just to let you know...I got "dunked" three times (and a partial little tease dunk). They pretended to dunk me as they were sending me up...then they actually did a little dunk. On the way down, two more dunks. But it was no big deal... you don't get fully dunked (head under)...just legs and maybe butt.
Let me know if you have any questions, I'll try to answer them from a "non-swimmer" point of view.
Hope you have fun!!
Ginny