On WinAPI, Sleep is denominated in milliseconds.
On BSD, sleep(3) is a library wrapper around nanosleep(2).
Linux's man pages make no mention of the magic number "1" as a "sleep 1 timeslice" shortcut; also, older Linux man pages warn that sleep(3) can be implemented in terms of alarm(1), which is used all over POSIX as an I/O timeout and would blow up the world if it alarmed in milliseconds.
If you want to sleep "as short as you can", sleep for 0 seconds, or call any other system call to yield your process back to the scheduler.