Hi Liopee, The answers above are lovely, elegant ways to solve your issue.
But I took a more simple approach and just duplicated the product page, which creates another product page, name it “No Price” and remove or hide the line that pulls in the pricing then I use that template when I add an item that shouldn’t show the price.
The catch is that you do have to remember to choose the correct template, but you also don’t need any complicated coding to do this. Just duplicate the template, name it no price, and use that template.
Follow along as I create your template here: https://www.loom.com/share/62cf5f320a754d4bb0492999f43638a2
Hope this helps.