I fiddled around with require and open::import(...) but that didn't made things better. Since, you want a lexical-region where STDOUT has UTF-properties, you could emulate that with a prototyped helper function that employed binmode and local to temporarily change STDOUT's behaviour:

use warnings;
use v5.10;
use utf8;

#-- prototype to setup a block where STDOUT is UTF-8
sub with_utf(&) {
  open(my $stdout, ">&STDOUT");  #-- STDERR analogue
  local *STDOUT = $stdout;
  binmode(*STDOUT, ':encoding(UTF-8)');
  shift->();
}


my $utf8 = "\x{3bc}\x{1fc6}\x{3bd}\x{3b9}\x{3bd}";

say "Default: $utf8";    # Wide character in say at 1048755.pl line 16
+.

with_utf {
  say "Lexical: $utf8";  # (no warning)
};

say "Default: $utf8";    # Wide character in say at 1048755.pl line 22
+.
[download]

Result:

linux> perl 1048755.pl
Wide character in say at 1048755.pl line 16.
Default: μῆνιν
Lexical: μῆνιν
Wide character in say at 1048755.pl line 22.
Default: μῆνιν

Seems, choroba had the same idea... ;-)