Clay contains high-low oils. Oils = pliability and adhesion ease. Oil is a solvent to the waxes/polymers.
Waxes are ultra-low in oils. Natures "gum", organic plastics. Without solvents, they remain rigid and have trouble with adhesion.
Mineral mud (hardening clay), uses a chemical reaction to harden, called oxidation and acidic-neutralization.
Polymers are nothing more than a mixture of all of the above properties. They can be non-hardening or hardening or waxy or gummy, but due to patents, don't expect any one form of polymer, except the most profitable to exist in a few years.
It sounds like you just want to use a wax... so use wax. NSP-hard is mostly wax. NSP-technical/manufacturing is about 95% wax. Depending on your climate and working conditions, you want to pay attention to the melting-points and softening/working-temps. Sounds like you want 108F softening with 130F melting-points, with low-oils/solvents.
NOTE: You can reduce the oil content in clays by simply heating them to workability, and pressing them between two pieces of brown-paper, or any paper. When they cool, the oils leach-out, and the paper absorbs the oils. This is called, "conditioning" clay. Never expect fresh clay to be perfectly workable to your personal taste. You can also microwave clay, to remove moisture. (Microwaves are targeted to water, thus, heat only the water within foods/clay. This will result in dry crumbly clay if done too often. The heat will destroy the chemical bonds of the polymers a little, each time.)
Also, on that same respect... You can soften clays by adding mineral-oils, a tiny bit of water to rehydrate the oils, or petroleum Vaseline (not recommended, as it is a cancerous petroleum oil byproduct.) And/or refined bees-wax or "sex-wax soft", used for surf-boards.
If clay says, "non-toxic", it should not contain sulfurs, as sulfurs are toxic, and thus, would not allow the clay to be marketed as "non-toxic".
Sculpey makes (EZ-Shape), which is a non-toxic kids clay. The kits sold with normal colors are more oily, the kits sold with neon-colors are more waxy with bees-wax "sex-wax soft" formulas. That is what I use for 90% of what I sculpt, after I have conditioned it to soft, medium, hard consistency. Being all the same brand, it sticks to itself without real effort, just enough to grip, unless worked-in to full adhesion.
Your body excretes oils which are a solvent to clay. Clay will always "stick" to your oily hot skin. Waxes will stick less, unless you are real hot.