Given that the bug report suggests only the is_W() function is used from FileHandle::Fmode I don't see why you can't replace the entire dependency with this short sub:

sub is_W {
    my $fh = shift;
    return 0 unless defined $fh;
    return 0 unless defined fileno $fh;
    local $\ = '';  # just in case
    no warnings;    # temporarily disable warnings
    #my ($atime,$mtime) = (stat($fh))[8,9];
    my $is_w = print $fh '';
    #eval{ utime $atime, $mtime, $fh }; # can fail if futimes not avai
+lable
    return $is_w;
}

my $file = "C:/tmp.txt";
printf "Null fh %d\n", is_W();
open F, ">", $file or die "Can't create $file $!\n";
printf "Writable fh %d\n", is_W(*F);
close F;
open F, $file or die "Can't create $file $!\n";
printf "Readable fh %d\n", is_W(*F);
close F;
printf "STDIN %d\n", is_W(*STDIN);
printf "STDOUT %d\n", is_W(*STDOUT);
printf "STDERR %d\n", is_W(*STDERR);

__DATA__
Null fh 0
Writable fh 1
Readable fh 0
STDIN 0
STDOUT 1
STDERR 1
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Update added "no warnings;" as per barts suggestion. Added comments containing mtime restoration code (if desired) also per bart.