Just a warning here - HDMI may support hotplugging on paper, but you should be very careful about doing it. I've HDMI<->something else adapters ruined for no apparent reason, and spent many hours scratching my head at what I thought were incompatible signals when the adapter was just dead and had been dead since the first time I pulled it.

I think it's something to do with the potential between two different earths. All computers and most monitors are earthed. External boxes like grabbers often aren't. But who knows really. Either give sacrifice to the HDMI god or turn things off before plugging them in to be safe.