Hi Ros
For me people asking to pay cash raise a red flag because they are trying to get around going through BnB (probably to save money).
There is of course no way of doing this through BnB and hosts won't be protected through BnB guarantee and if anything goes wrong BnB won't be able to help.
If I feel everything else is okay with the guest ie they have verification, full profile and are forthcoming about their plans etc and the guest is new to BnB, I will explain to them that I used BnB as it gives protection to both the host and the guest and give them the option to continue with the booking.
However if I end up declining the booking I would probably flag the guest to BnB.