The closest I can think of is to make a copy with all the content removed or unloaded from your game. Then you can run it in NW.js (or keep running in a browser).
The problem is NW.js is window based, and C2's multiplayer can't deal with multiple instances, so you'd have lots of windows open, and any overhead NW.js (just running it) has would be multiplied. Also as far as I can tell NW.js doesn't support running multiple instances by default.
In regard to rendering, you can't remove objects from the game obviously since it wouldn't sync with peers, and neither can you change the collisions or other properties without desync, so you are stuck with having those objects in. I'm not sure if this would help, but I imagine removing all transparency from sprites would help with decreasing overhead. That or (depending on how Canvas works*) blocking the whole layout with a fill layer to make the program think it's finished rendering when it gets to that layer.
*I have no clue how canvas works.
I'd recommend changing all the settings to their least performance-heavy options. I don't know much about performance, but I imagine this would be the most extreme you could get: