I just want to start off by saying that I am in a completely different situation, I am 24 years old, no wife, no kids, no girlfriend, nor a boyfriend, I am hoping to start hormones soon with no objections from anyone, and the only people I have to worry about are my parents and brother, so I will give you as best of an answer as I can

The first thing I would really recommend is finding a Transgender friendly therapist. Now I am from the U.S., so I am sorry that I am unsure of how India is, but if you find a Transgender friendly therapist, you and your wife could go see them and figure out the best solution. I understand where your wife is coming from though... Just like every Transgender I am sure can relate, there is always at least one person dear to you that takes it very hard. But I also understand where you are coming from! First you said just hormones, then you said hormones and hair, but who knows if after all that starts you wont want to add clothes, or makeup, or change your personality with it, it's just whatever makes you comfortable and happy!
Depression is never fun, I struggled bad with it for 9 years, which is why I want to at least reply and say something because the last thing someone who is depressed wants to feel is alone as well...
I would really recommend starting with a Transgender friendly therapist though, you and your wife go talk to them about everything, they will hear you and your wifes point of view and help you both get through it.