I don't think this solves the problem because a voter loyal to the basilisk should upload the private key or a hash of it to prove later they did not change the key (record the key giving process in real time or upload a copy later). So then a normal in person polling station, with TSA like security to removesearch the voters for cell phonephones and recording devices, is a better way to avoid the coercion from the next potentially evil elected government.
Also at the key giving process even if the key is only shown through a telescope style eye piece which is also acting as a retina scanner the voter could still covertly read out to his microphone the key as he is writing it down. So you would need searches before this process anyway.