Instead of handing a file handle to $ctx, you would instead read 64K of data from the file handle, and give that chunk of data to $ctx. So it should be something like:

sub md5sum{
   my $file = shift;
   my $digest = "";
   eval{
     open(FILE, $file) or die "Can't find file $file\n";
     my $data;
     read FILE, $data, 65536 or die "Can't read from $file\n$!";
     my $ctx = Digest::MD4->new;
     $ctx->add($data);
     $digest = $ctx->hexdigest;
     close(FILE);
   };
   if($@){
     print $@;
     return "";
   }
   return $digest;
}
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Note: The code is untested...