Child contact centres will have measures in place for parents who do not want to meet their ex partner, this can be discussed at the point of first contact with the centre or within your pre visit.
Not wanting to see or speak to the other parent of your children is quite normal when families start to use a contact centre. However, there will come a time when your children will need you to be able to cooperate with their other parent in order to give them the best possible chances in life. Therefore, it might be worth taking some time to think about how you might achieve this in the future.
In the short term a centre will support you in not speaking to or even seeing the other parent, if this is what you want. This can be achieved with staggered arrivals and departures; it is also possible for most centres to take the children from one parent in the waiting room to the other parent in the contact room. So, it can be possible for you not to have to speak to the other parent whilst using a centre.
Why not contact your local centre to share your worries with them? You might be surprised how much they can do to help.