Actually there is no (as i know) wallet that will let you make transaction with so low amount, but i think that i can suggest two options:

1. You can look for microtransactions services, and you have to open account there - when they collect little amounts from many users they are sending this. (it is very short description)
Ps. from long time i dont use services like this, so i cant provide actual links

2. You have to look for friend that is mining Bitcoin (he must have mining rigs). You have to ask him to which pool he is connected and if he agree, he can push your transaction for free (he will explain to you how to do that)

No more options.