From sleep,

May be interrupted if the process receives a signal

You could just go to sleep repeatedly until it's time.

# Optional, but a good idea with short durations.
use Time::HiRes qw( sleep time );

sub uninterrupted_sleep {
   my ($duration) = @_;
   die if !$duration;
   my $sleep_till = time() + $duration;
   while ($duration > 0) {
      sleep($duration);
      $duration = $sleep_till - time();
   }
}
[download]

Update: Bug fix. Changed $duration -= to $duration =.