I think it's worth noting this chart, showing that both nouns are about equally common overall...
(It's much the same with makes a noise / sound, etc.)
To the extent that there's a difference, noise implies unwanted sound.
Often that's because the "noise" is competing with wanted sound[s] (as in a signal-to-noise ratio), or because it's unpleasant / painful to hear (jet engines are noisy, not "soundy").
But sometimes (as in OP's context), noise is the unwanted alternative to silence (obviously anything the hitman might hear would be "unwanted" from Sean's point of view).
Thus for OP's specific example, noise is the more "natural" choice. But sound isn't "incorrect" - it's just a less likely stylistic choice that probably wouldn't carry even a fine nuance of difference.
However, it is possible to identify a fairly likely distinction between the noun choices, where they both refer to something that's definitely "unwanted"...
[My parents are upstairs, so...]
...don't make a noise
...don't make a sound
Obviously the exact circumstances of the person being spoken to would mostly dictate the precise implication of the noun choice (I'm sure you can think up some possible scenarios! :) But by default, native speakers would understand Don't make a noise as meaning Don't make loud / noisy sounds, whereas Don't make a sound always means Don't make any sounds / noises.