If you export the Webflow code and host it elsewhere, the only way to use the Webflow CMS with it would be to access the CMS via it’s API.
Another thing you could do is export both the Webflow site code AND the Webflow CMS data, import those to a host that also has a CMS and go from their.
An example of this would be Netlify.
That all said, it won’t be easy as all the “glue” between the Webflow site and the Webflow CMS will no longer work and it’ll be up to you to create custom code for all of that.