I have seen several videos of people completely disassembling laptops without anti-static wrist bands. Of course if you are working a carpeted room or on a rug, then it's better to be safe than sorry. But if the you standing on a hardwood / tiled floor then I don't really think you need to use one... unless you like rubbing your hands together in anticipation of tearing your laptop apart.
You will brick your laptop, it all depends of the degree of humidity you have in your room. If you touch any metal object and you receive a static shock, you will need a grounded anti-static wrist band. If you touch a ground before you open the laptop, and you don't put it on a wool surface like your bed, you won't have any problem.