The horror of the paperwork can unfortunately not be postponed, because the boat usually needs permission from local authorities and it is a condition of the insurance. Anyway, you will have to bite the bullet and fill out the necessary papers. For example, there are papers that are diving related and papers that are boat related.
But what do they want to see from you now? First of all, your passport, which you have to hand in. This is not because they are so sure that you will pay the bill at the end of the ride, but because they hand it over with a copy to the local authorities for permission to set sail. In addition, they naturally want to see your certificates and logbook, which is allowed both physically and digitally. If you choose the latter, make sure you have a photo on your phone and are not dependent on the internet.
Then there is the completion of the paperwork, the necessary indemnities, medical certificates and the like. Many people draw this blindly, they are tired and believe it all. But please take a moment to read through this as you will be asked to sign a contract. As a rule, this means that you declare that no matter what happens, neither the organizer nor the boat has any form of liability. Hopefully you will never need this contract, but ‘worse-case’ it is smart to have a photo of it, so just take it.
And then there is the medical statement with many questions about medication, your condition and whether you are trying to conceive, etcetera. As soon as one of those questions is answered with ‘yes’, you must submit a medical certificate from a doctor that indicates that you are allowed to dive. Don’t just fill in ‘no’ everywhere here, but prepare yourself and make sure you have that statement. Ultimately, this is not just a mandatory piece of paper, but again a release from responsibilities and can therefore be decisive in the aftermath about the costs of calamities. So take it seriously.