Is it possible to setup Webflow and WooCommerce on the same domain?

Is it possible to have the below setup?

On Webflow:
https://www.example.com
https://www.example.com/blog

WordPress + WooCommerce:
https://www.example.com/shop

The client wants to use Webflow for the main site and blog, and WooCommerce for the shop. What are the necessary configurations to achieve this setup? Should I use a reverse proxy, Cloudflare worker, or specific DNS settings?

Any tips would be greatly appreciated :raised_hands:
Thanks~

Update: I try using Cloudflare Worker with the below worker script.

But in this way, I have to switch proxy (the orange cloud) for the domain that points to Webflow hosting as well.

I am not so sure if the whole config works fine or not yet.

addEventListener('fetch', event => {
  event.respondWith(handleRequest(event.request));
});

async function handleRequest(request) {
  const url = new URL(request.url);

  // Redirect
  if (url.hostname === 'checkout.my.studio') {
    const newUrl = `https://my.studio/checkout${url.pathname}`;
    return Response.redirect(newUrl, 301);
  }

  // Route traffic
  if (url.pathname.startsWith('/checkout')) {
    const newPathname = url.pathname.replace('/checkout', '');
    const newUrl = `https://checkout.my.studio${newPathname}`;
    const newRequest = new Request(newUrl, {
      method: request.method,
      headers: request.headers,
      body: request.method !== 'GET' ? request.body : null,
      redirect: 'manual'
    });

    return fetch(newRequest);
  }

  // Handle other Webflow traffic normally
  return fetch(request);
}