Well, I don't think your question covers all the potentially helpful options here. Having ASD is only part of who we are, so therapy can often be useful, in my experience, growing up when no counsellors therapists or anyone much, factored in autism. I did a lot of therapy, which I paid for out of my earnings, and it helped me cope with life.
I also trained as a counsellor, family and relationship therapist, and learned a lot from this too. I subsequently trained others in these areas for many years. I came across interaction with young people with Aspergers and their families as a therapist relatively late in this journey, by which time I was able to recognise while reading about autism, the missing piece of the puzzle for myself.
Training in the area of autism is still rare for therapists. Therapy approaches have developed without much awareness of neurodiversity, and also have often suffered from problems such as competitiveness between their founders or developers, as to what is the best way to help clients.
Latterly this has begun to give way somewhat to recognition that there are a number of useful, well researched and well founded approaches that can benefit clients, and that the most important variables are 1) the specific needs, wishes and situations of the clients, and 2) the ability of the therapist to use the approaches in a way that is helpful to the client.
Sounds obvious? Well, many therapists would still argue that it isn't even true, and that their particular approach that they happened to train in, is always best... it's a baffling phenomenum, but maybe not so different from some other fields, or even some fields of science and medicine, where reputation and influence can sometimes slow progress that would be helpful.
So I guess I am saying, you won't necessarily get therapy that is different or that is delivered with an informed awareness of autism, although it's possible that you might.
On the other hand, therapy may be useful despite this, if it's reasonably well suited to you and your needs, and if the therapist is capable and respects you as an individual.
Plus, you may feel you would be able to be your own adviser and advocate in respect of effects of autism on you, and in making adjustments to therapy tasks or recommendations so that they fit you better. Ideally a therapist would want you to do this, if they do not have much knowledge of autism themselves. Therapy actually isn't something any expert can do to or for you, it really only works if the individual actively participates.
However in my experience, therapy that is delivered from a position that the therapist is the expert, is all too common. This can be seen as more like behavioural training, where you are taught to behave in certain ways so you seem more 'normal'. It doesn't approach you as a respected and unique individual, and is unlikely therefore to have any useful long term effects.
Specifically, CBT is great for some people, and not helpful or liked by others. It can also depends on the ability of the CBT therapist to deliver it, as to how helpful it can be. One variable I have noticed with clients reactions to CBT approaches, can be whether they prefer emotional recognition and approaches to approaches based on thinking things through.
If the former, CBT may not work well for them, as it is essentially cognitive and uses tools based on using thinking to change behaviours, whereas some people are more comfortable with approaches that start with their emotions, and help with their feelings. A good therapist can use CBT to help a feelings oriented person, or they may have other approaches to offer that are more feelings based, like EFT, emotionally focussed therapy, or similar.
Finally, what terrifies you about pursuing a diagnosis? It sounds like you think if you were to have autism, you wouldn't be able to change anything about yourself? This is not true at all. Autism is part, not all, of who we are. I have changed plenty about myself, over the years, and often without anything like the best help or the therapy I would have liked, but in quite effective ways nevertheless.
For example, one aspect of us is our ability to develop relationships with others. Research shows that people with autism have developmental attachment styles much the same as anyone else. This means that our security levels in relating to others can improve if we work in therapy to develop ourselves, and indeed if we just get some practice in relating and opportunities to spend time with others in ways we find useful or enjoyable. This is not about learning social skills, but about learning how to attach to others in ways that make us feel better, and that are mutually enjoyable. Many people miss out on learning how to do this in childhood due to parents being stressed, or ill or depressed, or for other reasons, such as poverty, or their needs going u noticed at home or school, which may apply to many with autism. But people with autism are able to improve their levels of secure relating much as Neurotypical people can.
When autism is said to be unchangeable, it doesn't actually mean you as an individual can't change anything about yourself. It means, you can't change that you are autistic, as opposed to neurotypical. There are some aspects of being autistic that won't change, in my experience these are around processing slowly and being rather disorganised, missing social cues, getting confused finding my way in new places etc.
Different people will have different effects of autism, but even these we can work around. It's like being left or right handed, or being good at sport rather than languages, it's just differences, and everyone is different.
Hope this is helpful, sorry it's so long!