Normally the klaxon was used.
18A5. Diving procedure .
The diving signal is two short blasts on the diving alarm, the second blast being the signal to start the dive. Two blasts are used to guard against diving on an accidental single blast.
An alternate diving signal is the word "Dive, Dive" passed orally.
http://www.maritime.org/fleetsub/chap18.htm#18A
Of course that would take a lot longer. I think the pumps and vents operating would make as much noise as anything to a listening destroyer. As for external noises carrying over the sea, I believe the klaxon could only be heard inside.
But I don't know for sure.