I would advise against using the small container for the following reasons:
1) The plating solution must be constantly replinished to the part, otherwise the available zinc in the container will quickly plate out, reducing the zinc metal to drop below an acceptable concentration, causing the parts to burn.
2) It is difficult to guarantee that the parts will not "nest" together, causing areas of the parts to be plated with very low thickness, if any at all.
3) Plating thicknesses will vary considerably since the parts will remain basically in their same position, even if shaken. The parts close to the outside of the container will have thicker plate than the parts in the center of the mass of parts, since the outside parts are closer to the anode (causing higher current density to these parts).
I know this is a long answer as to why not to use the container, but my intent was not to convince you, but to give you a few fundamentals about plating that you can use in the future.
I agree with Dedalus, that barrel plating would be more beneficial.