I know but in the event of a serious allegation of whatever kind having it could be useful and also on the occasion you just state that you are recording the meeting in order to listen back to the joy of being with your child, get it out into the open.
I have been in exactly this situation. A non family centre situation with supervision and notes taken. Notes that were outrageously skewed. I recorded and when notes were produced I was able to evidence factual inaccuracies. The role of the supervisor is to supervise so I didn't need to seek their permission to record because I didn't record them. And I did not need to get my childs permission to record him.