Hello
My website is divided in 2 main shops
Shop1 with Header1 and Menu1 and its products
Shop2 with Header2 and Menu2 and its products
Products not shared between shops
Sorry, but you could not avoid this because it is the default behavior when a product category is selected then the link takes to the default shop page that is set from WooCommerce Settings. And the menu on the default WooCommerce shop page header is displayed.
And WooCommerce doesn’t allow you to set two pages as a shop page you can set only one page.