I don’t think you’ll be able to pull this off directly. All of the admin screens, objects and hooks are tied to the “product” post type.
What you should probably do is add a new product type (a sister to the simple/variable product types). This new product type could be called “Custom_Type”. You can then add a field that lets you point to one of your custom post type objects.
This is a workaround. It means for every “custom type” you would also have a “custom type product” which references it. It’s not pretty, but it might work.