Cost to Add Closet in UES Co Op

I'm a first time buyer looking at a co-op with limited closet space. There is a corner space in the entry hallway / living room that could easily be turned into a small walk in closet (5x6). Since it's an existing corner, two sides of the new closet are already there, so I would just need to build the other two sides (one with a door). What would this cost? Can this be done by a contractor or handyman? Or do I have to hire an architect/engineer and get a permit through an expeditor? This is the only renovation needed on the apartment so hoping I don't need to jump through all these hoops just for a small thing.