The fog inside the shed will not effect the veggie garden…the "fog" will kill any spider that it comes in contact with… if the spiders are between 2 stacks of boxes sitting 6 inches apart, probably.. if the spiders are in the middle of a closely stacked pile of boxes, hard to say for sure…if the spiders are inside one of the boxes that are in the pile, probably not….. There has to be air circulation for the insecticide to be able to get to the target. The chemical in the fogger will only be a contact kill, it quickly breaks down. You may kill all the spiders in the shed with a fogger, but new ones can start re establishing the shed a few hours (actually can be less than one) later. Any pest control company working around your veggies can only use what would be safe to use around the veggies. You might also place out the sticky traps along the inside perimeter and corners to catch any crawling spiders.