You could just pretend to be your wife. I wouldn't worry about your voice and should the mediator query it. If they do, simply retort with:
“Are you suggesting I don’t sound like a woman? That seems an odd and rather inappropriate basis for identity verification.”
or
“I wasn’t aware that there’s a required way a woman must sound. Is there an issue with my identity or is this about the mediation?”
or
“That’s the first time someone’s questioned my womanhood based on my voice — shall we move on to the matter at hand?”
Do you get my point?
Considering that the context of the call is without prejudice and no direct interaction between parties occurs, the situation is low-stakes from a legal standpoint.
If you're still worried about it then you can take the call, tell them that your wife is unavoidably detained and say that she has instructed you to offer £0 and take it from there or to reschedule the call for another date when your wife could be available to offer £0.
Personally, I wouldn't worry about the first option. I do it all the time because our Sky subscription is in my wife's name but I am the one that deals with it and I eventually became fed up at having to have her come to the phone to simply say that she authorises me to deal with the issue. Instead I just started pretending to be her and I have never been queried about whether I am actually her or not.