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... (Budget: $150 - $200 USD, Jobs: HTML, Payment Gateway Integration, PHP, Stripe, Web Development, Website Design, WooCommerce, WordPress)