Hit Dice are not required to be spent during a Short Rest to otherwise benefit from it
A short rest is a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.
A character can spend one or more Hit Dice at the end of a short rest, up to the character's maximum number of Hit Dice, which is equal to the character's level. [...]
—Short Rest, Player's Handbook, pg. 186
Emphasis mine. If you were required to spend Hit Dice during a Short Rest to take a Short Rest, then the rules would expressly say so, perhaps with language like "A character must spend one or more Hit Dice at the end of a Short Rest in order to benefit from it". But they do not.
So if you're a Wizard trying to use your Arcane Recovery feature, or a Fighter recovering your Action Surge, or a Warlock recovering Spell Slots, or any other character that can gain additional benefits from a Short Rest beyond healing from Hit Dice, you can gain those benefits without spending Hit Dice.