Is it possible to remove hair and pigmentation at the same time?

I'm going to take advantage of the winter season when I wear long sleeves to start taking care of my armpits.
Frequent shaving not only causes hair growth, but also causes pigmentation, which darkens the shaved area.

It's a wishful thinking, but
I'm wondering if it's possible to manage two issues concurrently over the same period of time.
So, is it possible to get hair removal and pigmentation whitening (toning) treatments done at the same time?

Or should I get hair removal done first and then get pigmentation treatment separately?

If simultaneous treatment is possible, what is the ideal treatment cycle and recommended number of treatments for hair removal and pigmentation management?
If there are any precautions to take when performing concurrent procedures or any things to avoid to avoid straining the skin, please let me know.

Next summer, I want to have confident armpits.
I would appreciate your help in developing a treatment program and plan!