I've not used a lot of DK yarn but I do know there can be a fair amount of variation in WW, some of it I've used is closer IMO to DK. Maybe the same variation exists in DK as well. With sock yarn I've not noticed the variation, it's all skinny.
Cheating is an option. . . . Cheaters never win and winners never cheat, but smart knitters who want to retain an iota of sanity do, cheerfully. ~~Kory Stamper