From Star Trek: First Contact:
Picard: Initiate auto-destruct sequence.
[snip various characters giving authorization codes]
Picard: This is Captain Jean-Luc Picard. Destruct sequence: Alpha 1. 15 minutes, silent countdown. Enable.
Computer: Auto-destruct in 15 minutes. There will be no further audio warnings.
The computer's line is cross-cut with a shot of some random crewmembers evacuating into escape pods. It is clear that the announcement is audible throughout the ship, and not just on the bridge. So Picard didn't mute it to fool the Borg, for example (and there is no evidence that they were fooled in any event).
What was Picard's rationale for muting the countdown?
(The out-of-universe reason is obviously because they didn't want to run it down to the last second, and a countdown that doesn't almost run out is dramatically pointless. But I'm interested in the in-universe reason.)