Yes Cottonseed oil is used. I’ve used gear which was prepared with it.
Most vegetable oils are fine as long as they are USP, BP etc grade.
(USP: United state Pharmacopoeia, BP: British Pharmacopoeia)
The problem with the use of sesame seed oil and peanut oil is that many people have allergy; too them. I believe this is why cotton seed, grape seed oil and others are used.
The essential is that they are USP oils. Same goes for your solvents, preservatives and other agents, (Benzyl Benzoate, Benzyl Alcohol, Polysorbate 80 Polyethylene glycols)
They should be USP