It is totally possible to create custom categories page. However, you should remember that if you use static page for categories, the changes made in Ecwid control panel will not be applied to this page automatically. All categories info like image, name, description you will need to change manually, directly on the custom categories page.
Alternatively, you can generate custom categories list using Product API
functionality, which allows to get categories list dynamically. In this case, all categories’ changes made in Ecwid control panel will be applied to custom categories page automatically.
One more thing you should remember - you should exclude the possibility for customer to open standard categories page. As you correctly noticed, you should change “Continue shopping” button link and hide breadcrumbs links.
All these changes will allow you to use custom categories page.