Cooperation implies that one side has a higher ranking that the other. For example: The people cooperated with the kings request. Whereas collaboration implies more that the sides are neutral and will both add to the situation evenly. For example: The two kings collaborated to solve their problem. In your situation I would recommend collaboration because of its neutrality.

I think that Cooperation is more fit because its about a company. Cooperation is about association of persons who cooperate to their same social and economic benefit. Its more related to company.