Embed Woocommerce payment method in third party site?

I’m trying to figure out a solution for a client. They embed a donation method in their site, powered by Gocardless :
We’re exploring changing this over to a Woocommerce-based option, which would be run on a different web site, and so my question is do you know if it’s possible to repeat this embed method for the shopping cart process?
Thanks, Neil.