I am working on a website for a gym and the situation seems a bit specific. Namely, the gym owner wants to schedule appointments only, but without assigning trainers (staff). He wants to assign trainers who will hold scheduled training manually (after the booking process is finished and paid). This also means that it should be possible for several clients to schedule different trainings, for example, fitness, boxing, or weightlifting, at the same time slot.

There are different types of training (currently seven) and some are individual and some are group. Some group training sessions require up to three trainers, which is completely irrelevant; what is important is that they do not figure in the scheduling process because the owner will determine this later.

In other words, I want a potential client to choose only the type of training and a time slot and pay for it.

Please tell me if this situation is possible (meaning that the staff is not displayed in the site frontend) and what all I need. I also need a woocommerce integration to enable card payments. I need discount coupons as well but I would use the ones I have in woocommerce. 

I hope I explained well what I want.

Have a great day!