Ask supervisor *not* to come to viva?
In a UK viva, you are normally asked to leave the room when your examiners are deliberating your result. At this point your supervisor would also normally leave the room with you. As you said, they shouldn't say anything during the viva, and this should include any deliberation between your examiners. To be honest though, a supervisor does not want their student to fail, or have an unmanageable number of corrections, because that looks really bad on the supervisor as well. It's in their best interest for you to pass as easily as possible.

In the UK your supervisor is also never present without your permission. If your institution has these rules, then you can just ask them not to come. Just say that you feel it would add extra pressure that you could do without. It can be useful to have your supervisor there when you're read your corrections, as then they also know what you're asked to correct. In my viva I kind of got to argue potential changes during the viva, whilst we picked through my thesis. Since at this stage your supervisor definitely can't talk, you're in charge of your side of the negotiation.

Don't worry too much about changes. Your thesis only ever needs to be good enough to pass. It doesn't have to be brilliant, or better than anyone else's, it just has to demonstrate a significant contribution. You therefore shoudln't be asked to do more work for the sake of doing more. You should only have to change things if without them, your contribution isn't explained or supported well enough.

Remember that if your supervisor has supported your decision to submit your thesis, then there is little chance you'll fail. Try and enjoy yourself, you're unlikely ever to get to talk to two experienced researchers exclusively about your own work for such a long time ever again. Relish it!