Looking for a shopping cart for established shop

I have an established eCommerce shop that sells physical products. It already had product pages that can’t be changed i.e. example.com/category2/product4

I’m looking for a shopping cart/store that works with Paypal, my current theme, and can be integrated with my current products/pages theme. So if I create a product (orange football $20) I can then add it to my already made page at example.com/category2/product4 possibly via the product shortcode.

Ideally a shopping cart that doesn’t force it’s own product pages/URL’s.