VE, Segmented is the way they did it, joining several shaped sections around the rim, wagon wheels would then get a metal band that a Blacksmith would make a bit undersized and then expand it with heat and drop it over the assembled wheel then quench it by dumping it in water and the cold water would get the rim to contract around the outer rim and the exact steel rim contracting would also pull it all together, what you say about the spokes and the rim is correct, if I only wanted two wheels for a tea trolly then the easy way to do the rim is to laminate it, that is use a router to make a circular former the correct size, then cut and thickness the strips to a bendable thickness, say around 1/4 to 3/8ths of an inch, then layer about 4 strips around the inside of the former and clamp and glue it up but the hub would have to be made in two parts so it could be assembled however a tea trolly wheel has no load so that would be fine, 4 x 1/4 would give you a 1 inch rim so work out for yourself how thick you would want the rim/wheels to finish, there are some spectacular new glues, the wheels and rims would never come apart, I would go with segmented myself as that is the proper way that construction would be put together with all the spokes and hub in one go, use a giant compass to draw the rim as well as the entire spoke and hub detail and then decide how many sections you need for the rim, make a shaped jig so each section can be made with a router, you may need to make both an inner jig to cut the inner section and an outer jig for the outer section, if you work hard on the jigs construction the the created sections should just fit together, then assemble with a band clamp while it is all fixed to an exact circle so that when the glue is dry then you do have a circular wheel, drawn on a flat sheet of ply or just on your workbench top, making this type of a wheel is time consuming but very satisfying and is the same as making the wheels for a spinning wheel, all of this is work I wish that I had the time to do. I have wanted to make some spinning wheels for a long time and doing that is on my bucket list. NGM