Keep your apt as the clean room. Who's knows what organisms are living in that thing. Only assemble finished parts inside. Do not do any cleaning inside. Keep all parts organized in Rubbermaid bins. Clean outside and bring inside to dry and assemble.

Do not do any sanding of the cabinet unless in a controlled environment. An almost 50 year old cabinet probably has lead based paint ( or just assume it does) Even on a balcony one swift breeze at the wrong time or suction from you opening the door, and the dust is in your apt. Also your neighbors might not take to kindly to it either.