I had to do a bit of digging for this so apologies for a delay here.
You could potentially overwrite our cookie with custom code, but I wouldn’t advise it: https://stackoverflow.com/questions/4863740/change-cookie-expiry-date-http
If you’re worried about the cookie lasting too long, Google Analytics and Floodlight could be a good option for you: https://support.google.com/searchads/answer/7298761?hl=en
Hope that helps for now! Let me know if you have any questions