All fixed. Thank you for the suggestion. I edited your posted code slightly so that it just doesn't show the button at all (rather than inline). Now the only button showing on my cart page is the paypal express button which I set to be a text button (rather than the Paypal image) and set the text to Proceed to Paypal Express. The button picks up the themes css nicely and looks like it completely belongs. Again, thank you. Nice plugin. Here's the code that I pasted into my theme's custom CSS area (but could also be entered into the child theme's style.css):
.woocommerce-cart .wc-proceed-to-checkout a.checkout-button {
display: none;
}