++ operator can be applied to strings and then skip vowels:

use strict;
use warnings;

sub consinc {
  my $str = shift;
  my %vowels = ( 'a' => 1,
                 'e' => 1,
                 'i' => 1,
                 'o' => 1,
                 'u' => 1,
               );

  do {
    $str++;
  } while (exists $vowels{substr($str, -1 , 1)});

  return $str;

}

my $str = $ARGV[0];

print "$str - " . consinc($str) . "\n";
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update

'if' can do:

$str++ if exists $vowels{substr($str, -1 , 1)};
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