You will not be able to avoid AudioProcessorParameter, though AudioParameterValueTreeState is completely optional.
The wrapper class shows how all of the deprecated AudioProcessor methods relate to calls via an AudioProcessorParameter. You can simply add those methods to your AudioProcessor subclass (or probably just remove override keyword) and have the wrapper call those methods on your subclass. There really isn’t much boilerplate required at all to keep your core functionality identical to how it was before - calls to the deprecated methods will simply be routed via the wrapper.