What's wrong with just:

open( FILE, "$file" ) || die "Unable to open $file: $!\n";
undef( $/ );
$contents = <FILE>;
close( FILE );
$contents =~ s/\cM//gis;
open( FILE, ">$file" ) || die "Unable to write to $file: $!\n";
print FILE $contents;
close( FILE );
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Note: This is untested! :)