Is the special case exclusive? Meaning, is it a case the all objects of class 'Y' will behave differently based on the command-line switch? Or is it just once in a while?

Based on the answer to that you have two choices:

• Intermittent behaviour: your solution is an excellent one (extending won't work)
• Consistent behaviour: I'd change the constructor so that the method itself works differently

my $0.02