Your DM decides if this does not count as battle
The rules for Initiative state that
At the start of a battle, each combatant makes an initiative check.
Initiative is the first step in the combat sequence, the terms combat and battle are thus being used interchangably. From a perspective of games mechanics, when you make a single single attack you therefore are in battle, even if it is a sneak attack, and this will have the -10 DC for hearing the sound of battle.
Can you maybe use stealth on your attack to get around that? The rules for it state that
It’s impossible to use Stealth while attacking, running, or charging.
which makes it pretty clear that the game treats even a single attack as something that cannot be pulled off stealthily (with some exceptions for sniping, but that carries a -20 pentalty, not what you are looking for here).1
Now, narratively one can imagine that a normal battle with weapons clanging against metal armor, barbarians roaring and so on will be a lot louder than slitting someones throat from behind. It would be up to your DM to be generous and set a higher DC or grant you some circumstantial bonus for that. By default, favourable conditions grant a +2 bonus, bringing you to -8.
On top of that base DC, all kinds of other DC modifiers as listed in the description of Perception apply -- how large is the room and how far away are the allies next door? (+1/10 feet), is the door closed? (+5), are they distracted because they are playing cards? (+5), and so on. Your DM will have to set the final DC based on the overall circumstances.
1My interpretation why this is the case is that otherwise a high stealth character can sneak around and assassinate everyone with no risk of exposure, making this tactic unbalanced, for both sides of the DM screen. Assassination is a well known trope, but if it becomes so easy it cannot fail, it is no fun. I have experienced this with an optimized, high-stealth character in our group, which warped the entire game and put a lot of pressure on the DM to find mitigating tactics.