The person booking a dive fills in their own details

"They'll fill this in themselves" is for the other people on the booking. The person doing the booking is diving too, and on a dive that needs a certification they now enter their own date of birth, diver level, agency, certification number and last dive date before the booking is made.

Guests are unchanged — you can still email a form to anyone else on the booking, which matters when the organiser does not have everyone's certification numbers to hand.
The booker is told what it costs — choosing to email a guest's form now says plainly that they cannot get on the boat until it is filled in.
Your office is unchanged — staff still take a booking with whatever details they have and chase the rest, on paper or by form.