You certainly don't need the card PIN to make an online purchase. Just the card number/name/expiry/security code, those should be enough to initiate the transaction but the app should then ask you to authorise the individual transactions, either by the app password or biometrics.
It doesn't really matter if you have the "live" card or not, as soon as they issue a card number the details are on the app and it can be used whether you actually have received it or not.
I don't think any of this is only applicable to a Wise card.