We have other OS distributions that that live just fine on SD cards or sticks, already. If you want to bring computing to slums as a useful resource, the big problems are probably really:
1) actual hardware, shared or not, to run whatever open source OS you pick;
2) electricity to run the hardware and shelter for the hardware;
3) people to train those who have never used computers before, may have other literacy issues besides, and quite possibly speak dialects you will have difficulty getting localization for; and
4) affordable/free network access if these people want to use the internet.
I'll bet these are not the only issues, but if you don't address these, I suspect your money and time will be mostly wasted.