To remove a product from your website but still have it buyable, you need to ensure it isn't on your main menu or in any collection.

If you have a section for All Products on your main menu, you will need to create a collection with every product on your store except for the one you would like to hide from your website.

Afterward, add that collection to your main menu by selecting Collections like in the screenshot below:

After the product is completely removed from your menu and you have Online Store checked on the product page, you can share the product with people by sharing the Quick Checkout link of this product instead.