How do I permanently delete an app with NO OPTION of redownloading without re-paying

I'm giving my phone to my son, which is linked to my account. I don't want him to have an app that is currently on the phone and account (Whatsapp), so am trying to permanently delete it.(Have deleted off phone, and also on the computer, clicked delete and emptied recycle bin) but when searching for the app, I still have the option of downloading it (without re-paying).

How do I stop this? And make it so it is permanently deleted, and that if he were to delete it it would be charged (which would stop him doing it)

Thank you