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!

You have no control over whether your supervisor proposes wide-reaching corrections to your thesis. Even if he does, you might not know about it. After the viva, maybe you'll be given really wild corrections to make, and maybe they were proposed by one of the examiners. You have no way of knowing.

So, you are powerless, and you are ignorant. You cannot affect the outcome, and you will not even know what the outcome is. Rather than losing heart, take this opportunity to embrace it. This is something wholly outside of your control, and you are therefore free to ignore it. Breathe. Take a walk. Re-read your thesis. Enjoy dinner.

You probably will still be wondering, though. "But what if...?" "How can I know...?" "Maybe he'll..." Rest assured that your examiners are sensible people, experts in their field, and that they will know what is over-promising or outside the scope of your thesis. Your supervisor may suggest something in earnest enthusiasm, and the examiners may reject it, or settle for a more modest correction request. Your supervisor may decide to channel his enthusiasm into post-PhD follow-up projects with you.

tl;dr: Don't worry, be happy.

Just to add to the other good answers. You can always argue that a change is not needed or outside of the scope of your thesis. Your examiners will also know what they are doing so trust them as well, if they don't feel something is needed they won't push for it. The other thing is they will have a grade in mind when discussing it. If one examiner has minor corrections in mind they will push against suggestions that major changes are needed as this drastically changes the outcome. Finally they would also be less than ok with your supervisor interjecting as he should not be part of the decision making process, in fact he should be leaving when you are.

Finally while there may be nothing to worry about your own mentality is the most important thing. I know that nerves are not the most logical. If despite all reassurances you feel more comfortable with your supervisor out of the room then state this. You need to be comfortable in there, you don't need to lay out your reasons logically even to yourself. Just take the decision that makes you comfortable.

I feel there won't be an issue but you have to consider how you feel.