mindutopia has made some very valid points.
If there’s any chance your wife is delusional, or under an unhealthy influence, bringing in another form of therapy (any which way you can) may be very useful for everyone.
Normally I’d recommend ‘leaving kids be’ as you suggest, OP, but very little here is normal. The kind of session that your DS might sit through with a child therapist is very unlikely to traumatise him, or expose him to stigma. Is this what you’re worried about? You will have a chance to talk to his (private) therapist alone (even if it’s sneakily) to express your concerns and ask if there’s a way for the therapy to be framed as merely ‘a good chance to learn to express our feelings’, and that it’s important for everyone to practice those skills. They are always very careful with kids. Also make sure your wife has loads of time to express her concerns to ‘your’ therapist. It may be enough to get the ball rolling on investigating her therapist.
I can well understand your lack of trust in therapists generally, after your wife’s experience, but maybe try to see them as (as a group) as the solution to your problems, rather than the cause?
You need a champion to insert themselves between your wife and her therapist long enough to establish if there are issues in the methods he is using with her. Apart from his accreditations, other things can be checked from ‘inside’ the world of therapists. For instance whether he participates in supervision and professional development, or is linked to certain recognised therapy styles. Investigations can be made of his past, including complaints. Genuine therapists welcome these interactions and are used to them. If he doesn’t, it may well flag him within his profession and open avenues for you.
I think your wife will press for your son to be seen by someone. You may as well ensure it’s someone very qualified, experienced (and connected in the profession). Someone even your wife (or her therapist) can’t deny is an expert. Pay the money now, to get the best appointment possible for your son, in the hope that the whole situation unravels all the faster. There’s far more future risk to your son of trauma if this drags out, or your wife gets him sat in front of a mate of her guy.
And of course, keep an open mind that some real evidence may come to light (for your wife or your son). In which case getting him seen is crucial.
Good luck to you.