Yes an internet concert would be a good idea and he could play a mix of songs possibly not played before or seldom along with better known songs. Playing over the internet would eliminate his concern/comment about what he see when he plays a newer song (people going on beer runs, bathroom or cell phones going dark to stop recording).
He won't be able to see if someone doesn't like the song.
But I'm with some others who commented about the importance of song selection given his current voice and the possible need for other musicians to be present or playing to help smooth things out.