The reproduction was made with 8 ply 5cm x 5cm (2" x 2") gauze swabs. These look to be the same thickness as the original items.
8 ply is currently fairly standard for use as dressing material and in the operating theatre. One difference with modern swabs/sponges for use in operating theatres is that they have a radio opaque strip woven into them (looks like a black line across the sponge) so that will be visible on x-ray.
As you can see the original packet is fairly thin material and has bulged a bit over time. Maybe I should take the reproduction and kick it around the yard a bit
Here is one of the labels from the swabs I used.