Wax in itself does not inherently make leather stiff, maybe very slightly but not like plastic. Hot dipping leather will make it hard like plastic.
If you don't mind your leather darkening, I HIGHLY recomend "Sno-Seal"!!!!
I melt it and add a little more beeswax and some pine pitch, but it will do just fine as it is. It will make your leather waterproof and protect it.
Rub it in with your fingers, and use a hair dryer to melt it in. Don't over do it though, watch the sno-seal until you just see it melting. Use a back and forth motion, you don't want to cook the leather.
I use this exclusively to finish my sheaths, and boots, and jackets, and all leather. I don't use any stain, because I like the color that I get just from the sno-seal.
P.S. The best place I know to get sno-seal is at Big-5, if you have one close.