I remember hearing a story circulated a lot about a "weak" woman who went to vote at her local school and was seen by an M.S. who was working there as a janitor. Since he saw her voting, he was stumbled and ended up no longer going to meetings. Moral of the story was, we're watching you everywhere you go, so look out.
The only reason they tell you stories like that is because they want you to believe in their omnipresence and authority. The reality is, no one's going to see you. Try to think with your logical mind on this one instead of your JW mind. What are they going to do -- have teams of two JWs (because remember, you need two) stationed at every polling place in town all day? Are they going to be there with scope photography and video recorders in hand? Are they going to go to your town hall to get records on who voted? No, of course not. That would be stupid and a waste of their time, even being the gossipy zealots they are. They just want you to think they will.
Go vote. I've done it plenty of times and never been spotted. And even if I were, voting is not a DFable offense, and you could call them on that. If you're really that terrified, start with an absentee ballot and then go from there, but honestly, you don't need to.
According to Pew, something like 13% of all active JWs vote, and that's just the ones who admit to it. You know that percentage is higher in reality.