It depends on the model john deere. A 116 will have 10" slipfit wheels and a 316 will have 12" bolt on wheels
Standard GT rims are 5 bolt with a 4.5 inch spacing. width will depend on the specific tractor and back spacing of the wheel. I have some 12" wide wheels with a 40/60 spacing that will bolt up on some of my tractors, and some will rub. Gotta watch the bolt heads. It may look like you have enough room and drive it for a while. then you find out that you just cut a big groove in your new $100 tire.
The cart wheels you are looking at are gonna be 4 to 6 inches. just barely big enough for the front end and no where near big enough for the back end, unless you are building a lowrider racing mower.