No matter how strong your Hickory is, why are you considering making the legs less than 1 1/4"? 1 1/4" is reasonably small diameter. If it will support the 225 lbs. (probably more if it is hickory) then go with it without reduction. Stop the mental anguish and go with what you have read works. OR you can reduce the diameter and risk the whole project to save a few bucks. To say nothing of destroying the proportion "look" of the seat.. As a comparison, Shaker chair furniture legs are typically 1 1/4" diameter. However, Campaign furniture chair legs I've seen are turned larger than 1 1/4" and connected by brass screw in studs. I have seen camp tables that have thinner diameter legs, but not seats.
I'd dump Schwartz in favor of Nicolas Brawer and his book "British Campaign Furniture". It's a much better source, for the real thing.