### A strictly reading of the rules implies that using a skill requires an entire action.

In the [dedicated section][1] we have a list of options to use for the Action (*e.g.* Attack, Dodge, Hide, et cetera), but we can find the following bit:
> When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.

Moreover, there is [another part][2] of the rules about improvising an action (emphasis mine):
> Your character can do things not covered by the actions in this chapter, such as breaking down doors, **intimidating enemies**, sensing weaknesses in magical defenses, or calling for a parley with a foe. The only limits to the actions you can attempt are your imagination and your character’s ability scores. See the descriptions of the ability scores in chapter 7 for inspiration as you improvise.
>
>When you describe an action not detailed elsewhere in the rules, the DM tells you whether that action is possible and what kind of roll you need to make, if any, to determine success or failure.

For example, the highlighted part above implies that you are using the Intimidation skill.


In your case, you are improvising an action not listed in the Combat section of the PHB: using a skill falls in this "improvised action" framework, hence you need to take the entire action to use a skill.

This is confirmed in the [Ability Checks][3] section in the PHB (emphases mine):
> An ability check tests a character’s or monster’s innate talent and training in an effort to overcome a challenge. The DM calls for an ability check when a **character** or monster attempts an **action** (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results.



There are some classes that are able to use a bonus action to make an action (such as Rogue's Cunning Action), or the Fighter can take a further Action in their turn using Action Surge. In the depicted case, the Performance check cannot be done.

### The DM has the final word on it.
A DM could rule otherwise and decide that using some skill could be free. In some cases, this could ease the game and it does make sense (*e.g.*, during the movement make an Athletics Check for swimming in tumultuous waters, or something similar).

To be honest, in this case as a DM I would be very tempted to allow a player to adopt the depicted strategy because it is _very_ cool, but allowing it means that _all_ the player should be allowed to make a skill roll for free during their turn, and this could be really game-breaking in some situations (*e.g.* allowing a character to hide for free during combat).    


  [1]: https://www.dndbeyond.com/sources/phb/combat#ActionsinCombat
  [2]: https://www.dndbeyond.com/sources/phb/combat#UseanObject
  [3]: https://www.dndbeyond.com/sources/phb/using-ability-scores#AbilityChecks