All of this is fucking depressing, taken me a long while to start accepting it.
First and foremost no one can replace Chester, he was an icon, an amazing vocalist and a fantastic person. But the rest of the band are also great guys who deserve to continue their career in time, I'm sure that's what Chester would want.
I wouldn't want to see a hologram used, nor do I think a replacement could do most of the old songs justice, at least not in an emotional sense. So I can only really see the band continuing to play old Mike centric songs along with a bunch of new ones, which could either be with a new lead vocalist or a selection of guests.
In terms of old material they could still potentially play, there are the obvious earlier rapped ones like Step Up, High Voltage and It's Going Down, plus a few later ones that feature Mike on lead such as In Between, Hands Held High, No Roads Left, Roads Untraveled, Skin To Bone, Until It Breaks, Rebellion (with an altered bridge) Invisible and Sorry For Now. Maybe a few Fort Minor songs as well. That could fill more then half a set. You also have a couple of old favorites that could work especially with crowd participation, Papercut being one that springs to mind and In the End, where the crowd tends to sing Chester's parts very loudly and could be a nice nostalgic tribute to keep in the set.