Do the P&S 10.1 divergence results hold in scalar QED?

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Higgsy
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In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?
 
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Some hints: To show that proper verices with an odd number of external photon lines only, use the charge-conjugation invariance of QED, which holds for both spinor and scalar QED. For the four-photon vertex, use the corresponding Ward-Takahashi identity to show that it is finite at any loop order. Note that you have to combine all diagrams at a given order before you to the integrals to make this explicit for concrete examples of diagrams!