That sounds like an absolutely ingenious idea. My mum would get us to scratch her back as a kid. I later learned that she did this so we would open up more when we spoke to her as harder subjects are easier to talk about if distracted. Pool would be my choice x

Pool, a quiz, a walk in the countryside, bird watching. train spotting (!), going to see a match where you can chat but have a distraction.  ..Where cancer sufferers can get together but not just talk cancer. You can if someone wants to reciprocate but not in a closed psychologists room and have to talk about it all the time you can change the subject.  I live in the Sutton/Croydon so anywhere within those two boroughs for  me.  We could always get together at Maggies at The Royal Marsden first and if everyone feels safe and is agreeable organise something from there.  

I always feel like "I wish I'd said that" or worse, "I wish I hadn't said that" when I come out from seeing the psychologist.

Any takers.  Obviously there'd have to be a few responses before this is a serious option to pursue.