When you have established that a role is suitable for exclusivity, you don’t have to be absolute with your sell. Try positioning it along the lines of:

 ‘Mr Client, having discussed this role in more detail, I feel that it would suit an exclusive search and with this in mind, I would like to t spend a couple of minutes explaining why this is.’

You can then go through the relevant sales points for exclusivity, but if the client does not go for it, you still have the option of working the role on a non-exclusive basis.