I've reused a minimal part of it, mainly to get the same width and similar frame for other buttons. I went the cheap and quick way and grabbed the pixels. Basically, I first styled the Apple Pay button according to "Styling the Payment Request Button Element" and giving width: to <div id="payment-request-button">. When I was happy about that I grabbed a screenshot, edited heavily, and inserted the new graphics with width: and padding:. You can probably do the same thing with your own custom .css instead of pixels.
For the Apple Pay button so far so good, but in the Vivaldi browser on Windows the sleek Apple Pay button is replaced by this hideous purple thing of the same size. It will stand out regardless of other buttons being implemented by css or pixels. I'll work on disabling it.
Best,
Børge