Live projection with beamer during party

[Stab]

Hi guys,

One of my clients asked me if I can arrange live projection for them on a beamer + screen during their wedding party.

It sounds doable but I don't want to make it too hard on myself and for sure don't want to use the mini-HDMI output of my GH3.
Normally we use GH3's and GH4's for filming, but I might need to rent another camera for this. I don't think running a 20m HDMI cable into my GH3 is the solution but otherwise I wouldn't know where to start

So, what would be the best option here? I don't know yet which type of beamer it is but let's assume it has HDMI / VGA inputs.
Also, is there a wireless solution for this? And which camera would be suitable for this? 

Last question. I know almost every camera can output a liveview on an external monitor / Television but can it also do that to a beamer? Does it work the same?

Thanks!!