You can disable Apple Pay in iMessage by opening the App drawer, and swiping all the way to the right until you see the "More..." bubble.
From there tap on the "Edit" link at the top right corner.
You can then tap on the ➖ next to Apple Pay to remove it from Favorites, and then on the switch to the right to turn it off for iMessage entirely.
Tap "Done" to complete the process.
You cannot remove Apple Pay entirely from Wallet, but you can disable Apple Pay Cash. Just turn it off in Settings->Wallet & Apple Pay->Apple Pay Cash.
With that said, unless you've set it up and added a card for it, its not really going to do anything. It basically disabled.