When dealing with those older, heavier window units in tight spaces, the priority is controlled disassembly and proper drainage, since a sudden drop or yank is what usually compromises the internal plastic clips. Start by ensuring the power is completely cut off at the breaker. You want to isolate the unit before you even begin unscrewing the mounting hardware. Most units have a basic circuit, and those brackets are often tightened into the brick or framing itself, so loosening them in stages helps manage the weight shift. Don't try to haul the entire block off the sill; loosen the screws securing the housing first, leaving the primary bracket still attached to the masonry untill the last moment. For the actual lift and transport in a narrow opening, a proper two-person lift is usually essential, especally given how much they weigh. If you can, use a flat dolly or a heavy furniture mover with straps to distribute the weight and manage the descent from the sill. Never try to just drop it down, as that internal housing can shatter. Regarding your worry about moisture, this is more important than the removal process itself. Before storage, you have to ensure the condenser and evaporator coils are completely dry. Run the unit in fan-only mode for several hours just to circulate air and let the remaining moisture evaporate. Then, wipe down all accessible metal surfaces, particularly the coil fins. If you leave damp components inside a sealed unit, you’re inviting mold and corrosion that will eventually ruin the heat exchanger.
Once the unit is off and dry, if you are storing it vertically, make sure the drainage pan is as clear as possible. If you're worried about the brick or structural damage when you move it, taking photos of the mounting points before you start is a smart way to document the condition of the opening for later reference.