I have begun work on a set of authentic early Neolithic deer leather leggings. Before cutting the leather to make the leggings, I used it to quickly photograph what a simple leather wrap looks like. The leather wrap is so simple, in its most primitive un-decorated form, it may almost be simpler than the loincloth itself. It is simply a length of leather that has been scraped and generally tanned, wrapped around the waist like cloth, and fastened with a cord.
While it is possible the wrap could simply be tucked in like a towel, this is not very secure. Cultures with people who are known to walk around with cloth wrapped around their waist and tucked-in typically use longer pieces of cloth. Leather is smaller, and the point of the wrap is to not have to do any sewing.
As you can see, it is a simple, light and versatile garment. A man or woman who wears this will protect their legs while working but can easily remove it if they need to get in the water. It can be worn with leggings and other garments if the weather is cooler. It is effectively a skirt or a kilt.
Notice that the sides are tied in a bow, then the tight leather top is pulled down to hold the cord firmly in place.
Also, this is the back.
While the model that I use wears some body decorations and feathers hanging from the front, much more elaborate decorations could be made and the leather itself could be cut as needed. Here’s a picture of a better cut leather app which uses shells for decoration.