Can hashcat support zip2john's "$pkzip$" instead of only "$pkzip2$"?

[b8vr]

Have you formatted the hash for correct use in hashcat? Zip2john is for John the Ripper and does not work out of the box for hashcat. You need to remove any data from the hash after and including any : (colon).
Try hashcat --identify hash to have hashcat tell you what modes to try.