I can completely understand this situation. In fact it gives me anxiety while even reading it. But personally I feel it's ok to feel that anxiety and it is very common. As in you can't do anything about it. All you have to do is accept. It's completely ok to check with the client mentioning that your boss is unwell who was suppose to do the presentation, but you are going to take it on the behalf of him. It is even ok to mention that you have this tendency to get panic when nervous / if you don't want to show this side of yours to the client you can follow the below steps if possible.
In most of the cases we fear because of the "Spotlight". The fear of being "Judged". The only way to not completely carried away with the emotion is by spotlighting others. which is basically by putting questions to others. By doing this you break this pattern of you getting spotlight all the time. It doesn't have to be always a question even it can be something like "Hey, am I audible" / "Hey, does the screen brightness okay?" (It can be completely lame, no problem).
worstest case - you can always buy some time or request for a reschedule which is completely ok. But someday you have to do this so why not now.