Three responses.

My first one is that this smells like micro-optimization. In general micro-optimization is a bad idea. Keep your code clean and wait until you have a documented issue before you try to optimize it.

The second is that if you're only doing one thing with the sub, you can massively simplify your API to the following:

install_sub("is_inactive", sub {
    my( $self ) = @ARG;
    my( $realword ) = $self->realword;
    return $realword =~ $self->CHEVRON_QR;
});
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The third piece of advice is that when I have to work with hashes I sometimes find it very useful to use Hash::Util's lock_keys method to avoid trying to access a key that isn't there. Think of it as strict.pm for hashes. Sure, it is slower. But it is easy to make turning it on conditional. (Though unless I really need the performance, I usually just leave it on.)