Website builder that allows for custom payment integration

Hello lovely people of Reddit,

This might be an odd question, but I'm in the strange situation where I have my own payment technology / accounts but no website. I've been looking for a website builder where I could attach my own payments solution with a bit of elbow coding grease, but literally everything only seems to allow Stripe or whatever.

I'd really rather not pay those middlemen fees if I could help it.

I'm really just looking for something that already has shopping cart, inventory, and fairly typical ecomm features built out. I'd rather avoid Woocommerce and WordPress if I can avoid it.

Would appreciate if anyone has any suggestions.