Thank you so much! It is clear now that the button with the waitlist function (stock level zero feature) is not an add-to-cart button, so this is why nothing happened with the url redirect.
And thanks, the code helps to bring back the atc button, and thus the add-to-cart url redirect solution also works fine.
As we need to collect email addresses, at the end we added a Form in the product page Additional Info section (as Lightbox to appear as a button), and played a bit with spacing to have it where the act button would normally be. The button in the form has the possibility to redirect to a given url, which is the thank you page for us, defined as our conversion. If there is a better solution, let me know! Thanks a lot!