If there is no shooting through stall walls then a .22 long rifle (LR) is supposedly one of the favorites of real head-shooters. Additional detail might be the use a "subsonic" load that does not break the sound barrier (e.g. Aguila SSS, which stands for Sniper Subsonic).
A suppressed (silencer attached) semiautomatic (pistol) such as a Ruger Mk III (or slightly older Mk II) would be very quiet with that ammunition.
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