For efficiency purposes, you might want to keep the non-stringified regexp inside the hash. In other words, changing:

$hash{"$regexp"} = $value;

...
$value  = $hash{$key};
$regexp = qx/$key/;  # Expensive
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to

$hash{"$regexp"} = [ $regexp, $value ];

...
$value  = $hash{$key}[1];
$regexp = $hash{$key}[0];
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That way, you won't have to recompile the regexp.

OR! If you can't change the hash's structure, keep the compiled regexp in a second hash:

$hash{"$regexp"} = $value;
$regexps{"$regexp"} = $regexp;

...
$value = $hash{$key};
$regexp = $regexps{$key};
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