Conversion of a dumbwaiter to usable space in a NYC apartment is a popular idea but must be done according to NYC code. A dumbwaiter is a chimney, and as such must be sealed up by a fire resistant assembly. Use of plywood creates a fire hazard and is illegal.
Dumbwaiters may also be structural, or bearing, elements, and their removal may cause problems with the upstairs, or downstairs neighbors. Floors may sag. Walls may crack. If you plan to do this work make sure that you have the blessing, in writing, from the powers that be. Otherwise you may be liable for making repairs elsewhere.
Most prudent buildings require the shareholder to pay for an engineer’s report (typically $500 – $1000), and where I may be needed to make some probes in the walls in order to see what’s a bearing member. Keep these documents safe because structural problems may not show up for a year or so, and then everyone’s trying scrambling trying to figure out who is liable for the damages.
Dumbwaiter fire https://newyork.cbslocal.com/2018/01/08/riverside-drive-fire-upper-manhattan/
NYC Building code http://www.nyc.gov/html/dob/downloads/bldgs_code/bc27s18.pdf
sealed up shaft waiting for finish floor 
sealed up shaft with a chase for cables in the back 
1/4″ angle irons should be fireproofed with a coating of cement 
angle irons secured to joists on the other side of the chimney wall. 
metal deck to hold reinforced concrete 
metal deck and re-bar 
looking down 
looking up. An illegal conversion. 
dumbwaiter walls may contain asbestos fibers. The mortar certainly does. 
disassembled dumbwaiter shaft 
finish flooring
Technical drawings and correspondance with city officials
Seroy Inc. - contractor 