Damage caused by renters (us), options to pay from hosts [UK]
We caused some damage at an Airbnb. It was an accident, and we told the owners right away. We are not trying to get out of paying for it, but I don't know the best way to handle this. They are giving us the option of: 1. Paying outside of Airbnb (cash) for the damaged item and a minor installation fee, or 2. Paying through Airbnb's resolution process, but they have warned it will cost more due to 20% VAT (location js UK) and a "call out charge" (I am not sure what this means, maybe a tradesperson to install?).
I am looking for advice on which option to choose. We'd obviously like to pay the cheapest amount. I don't believe that VAT would apply to the damage invoice from Airbnb, and I think perhaps Airbnb would only require us to pay for the value of damaged item, not the cost of a new item. So I am wondering if the cash option is actually more expensive despite what they are saying. They have provided a receipt for the item so I don't have any reason to think they are trying to scam us. They seem very flustered and have said this is their first damage at their rental so they aren't sure what to do.