i've been to St John twice, and i don't think i ever saw a policeman there. so: unless you're hiding your consumption from the wife, i don't think there is any need to hide your beer.
EDIT: it's occurred to me that if you're staying at a large "respectable" resort with their own beach they may frown upon that, but if you're on a public beach (which 99% of them are), feel free to bring the cooler.
FOLLOW-ON EDIT: have you considered bringing a few beers in your suitcase, so you have something to switch up from the boring stuff you'll otherwise be drinking? if so, what does a beer aficionado bring to the beach? when i was last there i remember paying $13 for a six-pack of unremarkable lager, and $15 for what should have been a $6 bottle of wine. and this was from a grocery store.