I didn’t find any information in the forum about WP2Static except this, which is not that helpful, but does prove that Netlify can be used with WP2Static.
One thing you need to consider is if you delete your WP instance on your hostgator you won’t be able to edit your sites, you need to find CMS which is SSG (static site generator) friendly. You can check headlesscms.org for more options.
If you have a lot of text based content i would consider converting it into markdown (or other file based text formats) i would move the files to github or gitlab, then with an SSG like Hugo or gatsby i would generate the sites. The site generation can be done using Netlify Build.
There are CMS-es which can communicate directly with github/gitlab and are fully static (so Netlify can also host them, just as your site), so if an edit is happening the CMS makes a commit to your github repo (makes a change in your markdown files) Netlify can detect if a change is happening and can initiate a site build using your chosen SSG, the SSG generates the files from your markdown files, Netlify then copies the static files and your changes are deployed.
There’s an example repo which gets you going with all this, it uses NetlifyCMS and Gatsby, but there are other possibilities as well pending on your use case and content, etc.
Since you are aiming for a cost effective solution i would suggest to go with this path, but if you willing to go into more details about your site and how you’re going to use it, we can prob. come up with a more fitting solution.
One more thing: Don’t pair your Netlify sites with cloudflare, it could cause you issues and it doesn’t make any sense because Netlify is already a CDN, it’s already optimized and secure, it’s magic! 