Apple has a list of official URL schemes so that you can link to Facetime, SMS, Maps, and iTunes using a URL from an email or web page.
I want to be able to direct people to Apple Pay. I do not need to charge them, and am not trying to collect payment for anything. I just want to open the Apple Pay app with a click from an email.
How do you open Apple Pay with a click from an email or web page?
The URL scheme for Wallet (Passbook and Apple Pay together) is shoebox://, but that is officially an 'undocumented API' (source).
If you're trying to open the screen to initiate a payment, I believe that is possible only with a native app implementation and a lot of other back-end configuration.