Usually, a good way is to simply approach a company that offers a streaming service and ask for their help. A single event, ~100 people viewing.. it's chump change compared to some good publicity about helping a charity like that.
Mind you, you will still need a webmaster and other infrastructure to actually make a technical platform your event is based of off. Think of things like: donating online, somewhat professional looking video-editing, a big enough (and stable) pipe of internet connectivity capable of supporting your video stream, etc.