I managed to remove the battery without the adhesive by using the thread technique. More info in this video: https://www.youtube.com/watch?v=fupkPz55... . Just make sure you have someone to help you and hold the laptop in place for you.
After this step I continued from step 13, the steps in between were not really necessary in my opinion ( I succeeded the replacement without them). Just be careful not to touch these connectors during replacement.