Hello, welcome to FixYa.
Having done work for Asko for many years I can tell you you're not going to find a technical service manual on-line for these machines because Asko does not release them.
I can, however offer you a complete illustration of all the machines components including the control panel, thus you should be able to interpret how the panel comes apart.
To address the issue of the entire outer panel coming off, it is easier that way in my opinion, but whether it is necessary I think is up for debate...I usually remove it when I service them.
The sections you are speaking of are indeed "snapped" into place with the exception of the latch assembly and relatively easy to remove from the back. Here is an example of the illustrations I can provide (I can also guide you thrrough the process since I have changed a number of them first hand
Let me know if this may be of any use to you and I'll send it to you...though you need to post an email address with your reply if so. I'll watch for your reply.