I'm pretty sure that, even as a 5-piece, Mike will find a way to work in at the very least elements of all of the songs that he can't handle singing. Maybe mashups, maybe a medley where the crowd sings the parts that only Chester could have handled, etc.
For example, imagine this: The band finds a way to work in the chorus of OSC somewhere (knowing Mike it would be as creative as it is awesome). The lights shine on the crowd as they sing Chester's lines, and Mike does his own lines. Even small things like that would suffice I think, and would be a way to honor Chester's legacy and what he meant to the band. Moments like that could be worked in at various points during any given set that the band will perform in the future. Then again, I could be 100% wrong and they might do something completely different. A couple things that I know I'm not wrong about though? Linkin Park will still be Linkin Park, but continuing without Chester is obviously the end of an era. A sort of rebirth of the band is needed, but we all know that they will always find a way to honor Chester's memory as best they can moving forward.