Make your own out of MDF bases.
Rectangular for the base, sides and back and round for wheels. Cocktail stick or similar for the wagon pole. And Robert is your mother's brother!
Remember to allow for the thickness of the bases.
Different sized bases will give variety of wagon types.
Solid wheels are probably an anachronism but if anyone quibbles ask them for a contemporary image of the wagons at Adrianople!
I built the walls of a Sumerian city that way. Carts have to be way easier.