Originally Posted By: Jeanette_Isabelle
Either way, blade sharpening is a skill I need to gain.

That would be a skill worth learning in any case. You can use it for the kitchen knives too. Remember a sharp knife is safer than a dull one.

Originally Posted By: Jeanette_Isabelle
With that established, which is easier to learn: sharpening a razor blade or knife?

The proper answer is: It depends.
I would recommend a simple flat stone (I use this one: https://www.amazon.de/Fallkniven-DC4/dp/B004731IBG/ref=cts_sp_2_vtp. It is easy to use, does not require eletricity and is portable. It is also much harder to ruin the blade with a stone than with an electric grinding wheel.
Box cutter blades have a concave grind. That requires more skill than a flat grind (which many knives have). If you settle for a flat grind when resharpening, it is only a little more finnicky than a knife. You wil not restore the original sharpness though. It may still get sharp enough to pass the shaving test.
If it isnīt broken, it doesnīt have enough features yet.