Calendar inviation with responses but users are blind copied?

One of my users is having a golf outing and wants to invite many users - some inside our company and some external clients. They would like to be able to send them an invitation and have a response sent back to the chair with acceptance or rejection. I told them they could just send a meeting invitation, but they don’t want the users to know who else is invited. Now, there is an FYI (BCC) field in an invitation, but this does not allow the recipient to accept or reject the invitation - it just will add it to their calendar.

Does anyone have any ideas of a workaround for this? Any help would be appreciated.