Seagate sell a GoFlex Satellite which is WiFi equipped hard drive with a battery, it can create a WiFi access point which things like iPads or Android can connect to and play media from it, that might work in a pinch. Though the problem there is unless your camera can save files to network sources there is no way for them to access the video so you'd have to copy files over to the drive.
There might be something on the iOS app store that does it but probably only does it with the iOS device being your video camera.
If the Sony cam has a DLNA server built in that would be how to share the files over network, just get any DLNA media player for iOS like Airplayer or VLC and connect to the server running on the cam to access the clips direct.
EyeFi might be another way if the camera has an SD card but it will require a PC/laptop to act as storage, the EyeFi system auto transfers media after recording to the EyeFi server running on the laptop, then your clients connect to the laptop via phone/tablet to view the media. You can also use an iPad or Android device as EyeFi server so if it's just once tablet you need to use to show to others and camera has an SD card slot this would be the best approach.