Definitely use some sort of cloud server, I'd stay away from your VPN + port forwarding idea, it will only cause you issues. I heard good things about WooCommerce, it's FOSS. You can't get around JavaScript, it's impossible to build a functioning online store without some kind of JS. WooCommerce doesn't include trackers though, just the bare-minimum JavaScript that is required for the site to work.
How would you integrate with a payment processor? Handling payments yourself means that you would have to comply with the PCI standard and get audits in regular intervals, which are insanely expensive and only make sense if you actually run a large business which makes money from card transactions.
You don't have to be PCI compliant for stuff like bank transfers or other forms of payment. Credit cards aren't the default payment method everywhere.
Maybe it's pay on pickup, or just a simple mail with sepa wire transfer instructions.
Also, the PSP can still use JS but your site still doesn't need to have it. Services like Mollie and Stripe offer checkout environments they host, meaning you still don't have to use JS on your site.
Having a Stripe integration literally means having JavaScript on your site. Sure, it doesn't come from your website directly, but it's still loaded and executed when someone visits the site and tries to pay. TL;DR: Of course it's possible. Everything is possible. Having some FOSS JavaScript from WooCommerce isn't that bad though, and you'll likely need nonfree JS for payments anyway.