Replace CM13 recovery with CWM6
Will installing the CWM Recovery in fastboot mode break my CM13?


No, why would it? But before flashing your custom recovery make sure to disable the setting Update Cyanogen recovery or Update CM recovery or a similar setting under developer-options. Afterwards, flash your custom recovery the way you want. If that doesn't work, flash a custom kernel followed by your custom recovery. 

A custom recovery is not limited to a particular ROM so it doesn't matter whether you're using stock ROM or not.