Stripe Cloaking WooCommerce Setup

My RUO-peptide shop is already live on WooCommerce, but it cannot interact with Stripe directly. I have a separate, fully functional e-commerce site that is unrelated to peptides and I want every Stripe-facing process to appear as though it comes from this low-risk domain only.

Your task is to cloak the entire payment-gateway flow so Stripe (and any third-party compliance or anti-fraud tools) see nothing but the safe store, while customers continue to browse and purchase on the peptide site without interruption. The redirect or masking must leave zero forensic trace of the high-risk domain—no referer headers, no mixed-content calls, no metadata leaks, and no logs that could be pieced together later.

Key focus
• Payment gateway processes are the sole elements that need cloaking.
• Both the transaction itself and every step of on-site navigation tied to checkout must stay completely trace-free.

I am comfortable if you implement server-side rules, reverse proxies, Cloudflare Workers, custom WooCommerce hooks, or a bespoke plugin; whichever combination guarantees reliability and speed. Just make sure the solution is future-proof against Stripe updates.

Acceptance criteria
1. Initiating checkout on the peptide site calls Stripe exclusively through the low-risk e-commerce domain.
2. Browser dev-tools, Stripe dashboard logs, and server logs reveal no direct or indirect reference to the peptide domain.
3. All WooCommerce order data remains intact on the peptide store for fulfilment.
4. Normal site performance (TTFB and full-page load) is unaffected by more than 100 ms.

Please outline briefly how you plan to achieve the cloak, which technologies you intend to use, and the estimated timeframe for completion.