Does metal toggle switch in simple AC lamp circuit need to be grounded
Yes, I believe that such exposed metal should be grounded since it could become energized by a single fault condition where the metal housing inside touches, say, a loose wire. 

You can use a piece of metal between the switch and the inside of the wood to ground the metal parts, and connect that to the ground on a 3-wire line cord. Or use a switch without exposed metal. 

More metal inside would also slightly reduce the fire risk. I also suggest a fuse.