If he was born in Switzerland or has Swiss citizenship then he will be entitled to some level of disability insurance (IV) and he needs the label/assessment for that.
I would get a second opinion with someone who can assess him in his mother tongue. How did you find this psychologist? Did you get a referral from your paediatrician?
My understanding is that a psychologist can assess, but you need a paediatric psychiatrist to make the formal diagnosis. We have just gone through an assessment process with the school psychologist, Kjpd (kinder-jugend-psychiatrischer-dienst) and have therapy provided by the kinder-jugend-family psychologist unit of the unispital Zurich.
There is a very specialized autism specialist, dr gundelfinger, at the Kjpd in Zurich, if you are in Zurich I would recommend you ask your paediatrician to refer you to him, especially in 'borderline" or unusual cases.
Who is suggesting you delay entry to kindergarten? Are they authorized to make this suggestion? What did you specifically ask them?
As for assessing in non-mother-tongue, this is a big "no-no" in professional terms, although it might be a compromise, it is inadequate. All specialists will tell you that it is not ideal. What is his mother tongue?
As for the issue of,labels etc, if his behaviour is unusual enough for you to already seek professionals advice, and be worried, then the kindergarten teacher will quite likely spot him a mile off! A friend of ours just arrived from the UK and started school on Monday, was placed into language integration and by Thursday the parents had already been booked for an appointment with the teacher to discuss his developmental issues...
Regardless of labels or diagnosis, your child's teacher will have to work with your child 'as himself'. Even with a label, autism is a spectrum disorder, every child is unique and it will absolutely come down to the teacher-child-parent relationship.
From the bottom of my heart (and speaking from personal experience), denial, sweeping it under the carpet, avoidance or hoping it might just go away, is not helpful...there is a lot that can be done with really positive early intervention, and I have to say that our experience thus far is that the school system does have some very good strategies in place to meet individual children's needs...
Is he old, middle or young for the cutoff age for kindergarten? Has your child been allocated to a local school yet?
There will be two sides to the argument from the kindergarten, one would be to wait and give him more time to develop. The other would be to Immerse him in the language and social experiences as early as possible. There is the option of doing three years of kindergarten in Zurich, instead of two, and this can be done in consultation with the school teacher and administration.
Hope that helps!
You are welcome to pm me if you want more links or info. If English is the child's mother tongue then it should be possible to get a proper assessment done in English. I can give you a list of resources to try...