Right, the root issue here is trust. With a crowdfunding website, many people can give to one person, and one person can give to many people, and everyone can be sure that the person receives it, because everyone trusts the central authority -- the crowdfunding site.
But if you live under a dictatorship where your financial transactions are transparent to the state, then the state can step in and block any transaction. You need a way around that.
So I guess what you really want is to to set yourself up as an "offline crowdfunding site". So, maybe instead of building a network of people that you trust, you could build up a network of people who trust you to deliver the money to those in need.
There are numerous problems to overcome here, but I don't think that they are insurmountable.
One problem is just having the cash on hand, and thereby making yourself a target for attack.
Why not do a test-run with simple scraps of paper? Spread your idea around to your trusted network, let them know your idea, and ask them to ask their most trusted friends and family to get you as many scraps of paper as they would feel comfortable giving you if it were actual money?
Then count up your scraps of paper at the end, and then you'll be able to see if the idea will work.
Best of Luck.