I don't believe this is possible in the way you may want it.
Our users didn't like either to get the response email from WHD with all the notes. Many users will use their mobile devices to check their emails, meaning that it can be tricky to get scroll down to read the last note.
I believe in >settings >email >options there is "disable single-note e-mail". If this is ticket only the last updated note will go to the user.
The advantage is that the user can easily spot the information that was send, the disadvantage is that they can't see previous emails (comments).
But maybe this settings will help you already.
We found where to adjust this. Inside settings >email >options go to Outgoing email. We changed the Client email layout to simple. That removed all the extra fluff inside the message. We also unchecked "Include Recipient Section". On the tech email layout, we moved Notes to first. Makes it easier for our techs to see the conversations between them and the customer. It would be nice that this capability would be available for the customer, but that is not the case.