Variable product with and without fancy product

We sell metal buckles in our shop, which can be purchased by our customers with or without laser engraving and in different sizes.

 I have created a variable product in WooCommerce.

Attribute: with laser engraving / without laser engraving

Attribute: the different buckle sizes

I then generated the corresponding variations.
For all products with the attribute "with laser engraving," I assigned the respective Fancy Product.
The products with the attribute "without laser engraving" have no Fancy Product assigned.

The Fancy Product Designer is configured so that a product with a Fancy Product must be customized before purchase. The "Add to Cart" button only appears after a design is created.

I expected it to work like this:
Option 1: Customer selects "without laser engraving" + "any size" = Add to Cart button appears
Option 2: Customer selects "with laser engraving" + "any size" = Add to Cart button does not appear, instead "Open Designer" is shown

Unfortunately, this is not the case. The "Open Designer" button is always shown.

Is it even possible to configure a variable product so that some of its variations have a Fancy Product assigned and others do not?