I want to say around '54 or '55 is when the last skip tooth chains were used. CWC, Schwinn and I want to say Shelby and possibly other companies were using them into the 50s.
Prior to that, both types of chain were used simultaneously for a long time.
It seems to be a somewhat common misconception that skip tooth = pre WWII. Same goes for rear facing drop outs with adjuster screws. A few companies were still using those into the 50s as well.
Take Schwinn for example, typically using 1/2" pitch on higher end models, and 1" on lower end models.