It's not a matter of "hiding" the button. We completely removed this feature in version 4 since it's obsolete and outright dangerous with modern sites. The reliable way to change your database prefix is backing up your site with Akeeba Backup and restoring it. You can select a different prefix during restoration.
Changing the prefix on the tables while the site is running was fine in the Joomla! 1.5 days but nowadays it is NOT a good idea. If your server times out (we can't run it in smaller steps as this would break your site!) or if you have tables with foreign keys the process will fail before it completes. This will leave some of the tables converted and some not. The end result is that your site is broken and you need to use phpMyAdmin (or a similar tool) to fix it. This completely beats the purpose of using a tool to do this operation.
On the other hand, restoring a backup means that at this point the site does not run. We can do whatever we want in the database on our own time, knowing full well that any failure is not catastrophic: you can simply retry the process, probably with different time settings.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!