I’m not sure how to do what you want to do or if it’s possible. The way I do it is my Apple Pay cards are on the device I use to pay. For example, I can have certain cards on my iPhone, but they may or may not be on my MacBook Air. I don’t know how to pay with Apple Pay cards from a different device.
If you want to use Apple Pay on your Mac, I would add the card to your Mac. At least this is the only way I know how to do this. It’s under System Settings, then select Wallet & Apple Pay on the left side. You should be able to add cards from there. I believe when I initially set up my Mac, it asked what cards I want to add from my account but you can just click Add Card and it will show you a list of the cards you have on iCloud. On mine all are selected by default. Unselect whatever cards you don’t want to add and then press next. Have the physical card ready because I believe it asks for the CVC number on the back.
If there’s another way to do this, please someone let me know, but I’m not aware of it