I agree with Sara,
Talk it over with your therapist. First, to determine if they would diagnose Gender Dysphoria, or perhaps something else. The reason for the diagnosis is to make sure that nothing else is influencing your thoughts.
If they feel that is what is going on, they can help you decide how and when to approach your wife about it. Perhaps she can come with you to a therapy session. That allows her to hear it from the therapist, who can answer her questions about it. That also puts you in a position to hear your wife's questions, so you have an idea about how this news is affecting her. The therapist can work with both of you to get through it.
Think about it like this:
Would you announce to your wife that you think you have cancer, or would you get a diagnosis first?
One of the thoughts that ran through my head was, what if the psychologist is wrong (all four of them)? How do you go back to your family and say, Oops, no false alarm? Then they wonder why you thought that in the first place.
Wait until you know enough about the situation to answer some questions, and see if the therapist can advise you.
Just my two shillings' worth.
