If you have a high speed Dremel like tool, these with an abrasive attachment are very effective at physically grinding off the hard skin. Of course you need to avoid pressing it too hard onto your skin as it will generate heat from the friction.
You may apply something like KY jelly or moisturiser to your skin it will soften it and provide some protection against heat. Otherwise a wet towel or a spray bottle can be used to douse any heat sensations instantly. On that front the heat is only very localized and dissipates very quickly and does not result in any burns.
I know it sounds odd to use a 30,000 RPM tool to remove hard skin but myself and friends find it effective. Which tool to use is up to you really,obviously avoid anything like a cutting disk attachment, anything for grinding is most likely ok. Just be sure you aren't going to cut yourself with the tool head if you screw up, so sanding barrels are always safe on that front.
Also finer grits aren't always better depending again on heat being generated. You wan't to get it over and done with quickly but you don't want to hurt yourself just learn what is an acceptable tool and method that avoids heat. Example don't press down over a single location keep moving, and the heat generated will be spread around