No, you don't "pay for it" with the attack, it's just not something you can do simultaneously with the attack. At no point is it established that you have to be able to attack in order to use the power and it's definitely been tested the other way.
We can ask the four playtesters here (or the three who are still active), but I'm pretty sure my and Karat's interpretation is the intended one.
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Arkham
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Ronin
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Lazy Orang