Opting out of open source licenses doesn’t mean you’re opting out of copyright law.
You’ll have to check with your own legal counsel regarding your particular project, but generally speaking, the absence of a license means that default copyright laws apply. This means that you retain all rights to your source code and that nobody else may reproduce, distribute, or create derivative works from your work.
You don’t have to do anything to not offer a license, though including a copyright notice is recommended.