What this requires is up to your DM
Most importantly, you don't get to decide you want to make a Performance skill check. You can narrate that you want to drop down and simulate snoring, and then your DM decides, if that just works, or if you would need a skill check for it, and if so, if it requries Deception or Performance.
This goes back to the fundamental loop of the game (p. 6 PHB):
- The DM describes the environment
- The players describe what they want to do.
- The DM narrates the results of the adventurers’ actions.
Because of this, your DM will have to decide if you need to make a check, or not, and if so what kind of check.
General consensus is that there is no rule that every use of a skill requires an action in combat, as explored in depth in: In combat, do all skill checks require an action to perform? and also here: Do ability checks in combat require an action?
Most DMs require an action for skill checks in combat, but the choice is up to the DM. So if they agree that you can try a Performance check, they also need to tell you if that check requires you to use your action.
The text of the rules sometimes uses action in a less formal way than the defined "your action" for the turn in combat. For example, the section "Other Activity on your Turn" (p. 190 PHB) advises you
Your turn can include a variety of flourishes that require neither your action nor your move. You can communicate however you are able, through brief utterances and gestures, as you take your turn.
The inset box "Improvising an Action" (p. 193, PHB) tells you
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 for a parley with a foe.
So what is calling a parley now? On one hand, the rules tell you it is an improvised action. On the other hand, all you need to call for a parley is to shout "Parlay! Parlay!", a brief utterance if there ever was one, that does not require your action. Because of the ambiguitiy of what is or should be sufficient to affect the action economy among the countless possible things you can try, the DM is called upon to adjudicate.