Not necessarily because you are not shifting your weight. In most cases where only the woods are slicing, I see ball position being the main problem. Make sure it is on or about the front toe.
Irons like to be more centered in the stance to promote a decending angle of attack. Woods like to be swept in a shallower angle. But, slicing is caused when the face does not get square prior to impact. So moving the ball forward give the face more room to go before it strikes the ball and could solve your problem.
If you have a good ball position, then look at the next major cause: Over hitting the driver with the arms.
Irons don't get over hit because you are trying to go an exact distance. But the driver is meant to go maximum distance so we swing at a maximum level which is most often over your controlable level. The arms get used excessivly and they get ahead of the rest of the body and shoulders and your hands cannot catch up leaving them behind with an open club face. The trick is to make a strong move with the hips and shoulders to the ball and let the arms go with them, and not ahead of them.
Hope this helps.