If you're in the UK, you can leave the power-lead plugged in, just switch the power off at the wall if possible, that will keep the case earthed (grounded). I'm not certain about the USA, I think they only have 2-pin power-sockets.
While working inside the case, I've found those wrist-straps to be a PITA, just ensure your hand/wrist/bare-skin is touching some case-metalwork - It's easier to touch the case than not, in most instances