I want to change my game to master mode, (BOTW DLC) without deleting my save file. The reason is that I want to change my white lynels to silver and silver to gold. I'm pretty sure you can do that. I'm not sure how, though.
To unlock Master Mode, you must purchase and download The Master Trials (DLC pack 1). After doing so, you should see an option to start "Master Mode" on the main menu.
Selecting Master Mode for the first time will start you with a new game. It is not possible to switch your current save to master mode. However, starting in Master Mode will not clear your current save. You will be able to toggle between your normal mode save and your master mode save on the main menu.