[endswapper]

Yes, you should speak in the YC video.

If your startup finds any reasonable degree of success in the US (given you are applying to YC, and perhaps other accelerators in the US) you will need to speak to prospective investors, and perhaps industry or trade groups, if not consumers directly. Consider this the first the first step getting comfortable doing it, which seems to be the problem.

As far as YC and rejection, the video, in part, is supposed to give them a read on how you guys interact. Not speaking certainly limits the amount of information you give them to do that accurately.

In the context of the team and how you guys interact I recommend considering your partner's input very seriously. If he is in favor of you speaking, and there is a significant practical reason, such as specific domain experience, you have to balance your discomfort against submitting the best possible application.

There will likely be many more items such as this and it's best to confront them, fail, learn, move through them and move on.