#!/usr/bin/env perl
use strict;
use warnings;
my $total_sleep_time = 0;
BEGIN {
*CORE::GLOBAL::sleep = sub(;@) { $total_sleep_time+=$_[0]; CORE::sleep($_[0]) }
}

# use this module and the other
# ...

print  "\$]=$]       \$^V=$^V\n";
sleep(2);
print "total sleep is $total_sleep_time\n";