Hello
It depends on what type of data and which partition you're planning to delete.
If your computer is functioning smoothly and you can work with all your apps and files without any issues even after disconnecting your old disk, it could be safe. However, you may need to be very careful as there might be some files that you may not be using now but sometime in future you may come across a few errors stating some missing files.
Please report back with more details to allow us to provide you with a more narrowed and precise solution.
Cheers!!