Just replace this:

        tie my @file, 'Tie::File', $File::Find::name or die "Can't
+ tie $File::Find::name $!";
        splice @file, 0, 4;
        untie @file;
[download]

with:

        open(F, '<', $File::Find::name) or die "...";
        my $tmp = $File::Find::name . " - new"; # see comment below
        open(G, '>', $tmp) or die "...";
        for (1..4) { <F> }; # don't copy the first four lines
        while (<F>) { print G }
        close(G);
        close(F);
        rename($tmp, $File::Find::name)
            or warn "unable to replace $File::Find::name: $!\n";
[download]

The only caveat is that you have to ensure that $tmp can never be the name of an existing log file.

The tie method is inefficient because it reads the entire file into memory.

One advantage that this approach has over an in-place re-write is that you won't have to worry about leaving yourself with a corrupted log file if the copy is interrupted.