for (glob "$path/*">) {
    unlink if -f and -M _ > $cutoff;
}

##</code><code>##

sub unlink_all (
    my ($path, $cutoff) = @_;
    local $_;
    for (glob "$path/*") {
        unlink, next if -f and -M _ > $cutoff;
        unlink_all($_, $cutoff) if -d _;
    }
    1;
}