I have done a bit of work with early velocipedes and wooden wheels over the past few years. There are several things I see about these wheels you show here or those wheels affixed to that rocking chair. If you look at say, the Sterba website, at the early 1800s hobby horses, you will first notice how crude those wheels on some of those machines are; very crude, home made, toy like almost, and maybe that is part of where the name hobby horse comes in- although these machines were built back in the day as a means of transportation, they were to a degree regarded by most as kind of a novelty, and maybe not something you would go traveling many miles on (although as it is known, some certainly did). They were almost like a toy or gadget that more well-off people might have, and maybe that why they didn't catch on in Europe more than they did until the advent of actual functional bicycles, and far as I know, never in America.
Regarding those wheels you have considered, I think they may actually work, but you will have to do a lot of improvements to them, however, you could possibly save a lot of money. If Stutzman built you a set of comparable wheels, you would be looking at the better part of $1000, and his work is so refined, it might not be quite what you are after if your looking to build a crude style hobby horse.
If you bought those $59 dollar wheels, keep this in mind. You would have to at a minimum, totally dismantle them. Inspect the existing joinery of the spokes, felloes, and hubs to ensure that the existing joinery is adequate to hold the wheel together. The hubs look a bit thin, and may need reinforced or perhaps new thicker hubs made, which you could do. The felloe sections which are currently held together and in place with metal fasteners; the metal fastners will have to be removed, and replaced with splines, mortised into place in the outer tire side section of the felloes, and then felloe bolts installed one or two per felloe through the tire. As for the steel tire; you will have to fabricate that by purchasing at a hardware store some 1/8 inch or so thick, steel bar stock, and then bending it into a perfect circle, welding together the joining edge. You will then have to hot set the tire correctly. You will need to fabricate a bushing for the hub, which can be done ideally with a bronze bushing, however steel pipe can be used, and then this, pressed into the center of the hub. Ideally, you would weld onto the pipe, a couple of short fins so that once the bushing is inserted into the hub, the bushing wont rotate in the hole. You will also need to make a couple of steel hub bands and hot set those onto the hub on either end to prevent splitting.
If I am not mistaken, when I sized and set a steel tire on an original wooden velocipede wheel, the measurement I used for tire size was, for the outer circumference of the wooden wheel felloes, to be two tenths of one percent larger, than the inner circumference of the steel tire. In other words, where the tire is only just barely smaller than the wooden outer part of the wheel, to where it just barely wont go on when cold, hence the need for hot setting. That steel tire is entirely what holds the wheel together
I know that sounds like a lot, but it is not really too bad, and it could be done, but that is really the bare minimum that would have to be done to make those an even more or less functional set of crude wheels. You would save a ton of money, since the extra steel parts I mentioned would not set you back but another $50 -$100 or so.
