Nothing beats wood for ease of duplicating wood. Wood is a very old modeling material, is still around and plentiful in hobby shops. Yeah, you can use plastic finished to look like wood, but why? I'd use basswood rather than balsa. Balsa is fine for airplanes that need to fly, 'cause it is so light. But basswood is a better wood for workability. Again, most hobby shops carry a range of basswood sizes.
Depending on style of wheels and axles, plastic wheels are available in 1:24/1:25 size for a cart of that vintage. Many 20th century carts used automobile or truck wheels and tires.