my @groups;

while (<DATA>) {
    chomp;
    next unless /\S/;
    if (/^#/) {
        push @groups, [];
        next;
    }
    push @{$groups[-1]}, $_;
}

while (@groups) {
    my $group = shift @groups;
    my $ip = splice @$group, rand @$group, 1;
    say $ip;
    push @groups, $group if @$group;
}

__DATA__
... your list goes here ...