• I show a different indenting style below, but that is no big deal to me.
• More important to me is: $href->{key1}{key2}I think that reads easier than use of $$href{key1}{key2}. My preference is to only use $$scalar_ref to de-reference a scalar value.
• I replaced $& with a simple $1 capture. There can be some performance issues with $& with Perl < 5.20. See perlre. My preference is not to use $& unless needed, and here it is not.

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dumper;

my $str = 'a[bdy]dfjaPÑsdafÜ';
my $str_2 = 'WAP';

my $hoh_ref = {
    hash_1 => { a => 'a[bdy]dfjaPÑsdafÜ',
        b => 'WAP' },
    hash_2 => { c => 'Te st' }
};

print "Original Hash:\n";
print Dumper $hoh_ref;

foreach my $main_key (sort keys %{$hoh_ref}) 
{
   foreach my $sub_key (keys %{$hoh_ref->{$main_key}}) 
   {
      if ($hoh_ref->{$main_key}{$sub_key} =~ /[^[:print:]]/) 
      { 
         while ($hoh_ref->{$main_key}{$sub_key} =~ /([^[:print:]])/g) 
         {  
            print "Non Printable Character:\t$1\n";
         }
      }
      elsif ($hoh_ref->{$main_key}{$sub_key} !~ /\s/) 
      {
         delete $hoh_ref->{$main_key}{$sub_key};
      }
   }
}

print "\nResult Hash:\n";
print Dumper $hoh_ref;

__END__
Original Hash:
$VAR1 = {
          'hash_1' => {
                        'a' => 'a[bdy]dfjaPÑsdafÜ',
                        'b' => 'WAP'
                      },
          'hash_2' => {
                        'c' => 'Te st'
                      }
        };
Non Printable Character:    Ã
Non Printable Character:    ‘
Non Printable Character:    Ã
Non Printable Character:    œ

Result Hash:
$VAR1 = {
          'hash_1' => {
                        'a' => 'a[bdy]dfjaPÑsdafÜ'
                      },
          'hash_2' => {
                        'c' => 'Te st'
                      }
        };
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