I notice that you read all the words into memory, even though you only want words of a single length. You can save memory by filtering out the other words as you read:

while (<INP>) {
  chomp;
  push @chk if length == $word_length;
}
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On the other hand, you might like to make this an interactive script, which reads in all the words, and then prompts for commands from standard input in a loop.