Werbil,
You may well be correct about the insurance. Aviation insurance isn't an area in which I have a great deal of experience.
I suggested PI because if The Contractor dings it, he needs to be insured to sufficiently cover a claim arising from The Principal (or some other plaintiff) that the damage was caused or contributed to by a poor operational decision, error or an omission made in the course of The Contractor's service delivery. PI will cover that.
If some other form of insurance is available that covers damage to an aircraft The Contractor doesn't own but is using in the course of his business, then that would probably be more suitable. Not sure if hull insurance covers that sort of thing, but there may be some insurance product out there that does.
Does public liability cover it? Maybe, but you'd have to check the terms and conditions carefully. Often public liability claims may only be actioned to cover injury or damage to third parties, ie an entity that has suffered loss or damage, but is not a party to a contract or transaction (say, a member of the public - hence it's name).