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use Encode qw( encode );

...
   or die("Can't create \"$qfn\": $!\n");

print($fh join("\x01", map encode($encoding, $_), @values));

use open ':encoding(UTF-8)';

...
   or die("Can't create \"$qfn\": $!\n");

print($fh join("\x01", @values);

use open ':encoding(UTF-8)';

...
   or die("Can't create \"$qfn\": $!\n");

print($fh "$_\x01") for @values;

use open ':encoding(UTF-8)';

...

local $\ = "\x01";
print($fh $_) for @values;