Pin length, diameter, and face/file profile are all relevant. The diameter and face profile are the most important dimensions, but if the length is way off, you can have problems as well.
The last time I used substitute pins on a New World, I used English pins produced by Hercules Cycle & Motor Co. These were Birmingham Hercules (not Nottingham Hercules) pattern pins. Over the years, I accumulated a tin full of old cotter pins from various bikes, mostly English ones. If I recall, I tried various pairs and found the Hercules worked best. Eventually I located a couple pairs of original New World pins and replaced those Hercules pins with original Schwinn pins. The fit was basically the same. I suspect when Schwinn developed its parts for the New World, they based their dimensions heavily on English bicycles of that era (1930s).
I'd look for a set of non-Raleigh English pins. The face profile requires a lesser filing than the more aggressive filing done to Raleigh pins. Bikesmith Designs may be a possibility as well.
I probably have a pair or two of the New World pins in the tin somewhere. The tin is still packed away with my parts from when I moved earlier this year. If you end up needing exact dimensions, I can probably come up with them. I do recall setting calipers to a nearly new 1940s Schwinn pin and had recorded all the specifications. I don't recall where my spec sheet for it is.