Maybe disabling the warning locally is the less cumbersome solution:

{
  no warnings "uninitialized";
  debug("x='$x', y= '$y'");
}
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(Or with the no warnings inside the debug function if you use the hash version).

But actually, if the purpose is debug, being able to tell the difference between undef and the empty string is probably useful. Maybe with Data::Dump:

use v5.10;
use warnings;
use Data::Dump qw( pp );

sub debug
{
  if (@_ > 1)
  {
    say pp { @_ };
  }
  else
  {
    say pp $_[0];
  }
}

my $x = 23;
my $y;

debug([$x, $y]);
debug(x => $x, y => $y);
debug("Hello");
debug("Hello\n");

__DATA__
[23, undef]
{ x => 23, y => undef }
"Hello"
"Hello\n"
[download]

It also displays \r \n that might go otherwise unnoticed (eg: you have the two when you only expected \n)

Edit: corrected link to Data::Dump