Some maintainability may be gained at the cost of some concision by separating out loop list generation:

my @keys_to_process = $x eq 'key_1'       ? keys %my_hash
                    : exists $my_hash{$x} ? ($x)
                    : ()  # default - nothing to do
                    ;

foreach $key (@keys_to_process) {
    do_something_with($key);
    }
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Further, because the above will loop over all keys if $x eq 'key_1' is true even if 'key_1' does not exist in the hash (which may or may not be what you want: Your Logic May Vary), perhaps re-order list generation:

my @keys_to_process = ! exists $my_hash{$x} ? ()
                    : $x eq 'key_1'         ? keys %my_hash
                    :                         ($x)
                    ;
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