What we would want here is to design a way for these people to be able to register while making sure it does not become a vector of attack for malicious entities.
The fact that you need to speak in your video submission is because it adds a layer of security in the ways challengers can detect potential malicious duplicate profiles. You cannot simply say that some individuals are allowed not to speak in their submission or any attacker would exploit that breach.
It is also very complex to ask submitters to provide proof of disability.
We could allow video submissions where the person who cannot speak appears in the video with another person that tell the sentence for him/her. The person speaking on behalf of the other could be required to be previously registered in the registry and to be the voucher of the person who cannot speak.
I think we should also limit this mean of registration by allowing any person in the registry to only help the registration of a single other person he vouched for in order to prevent malicious actors from exploiting numerous people and control their profiles.