No you don't need iTunes. I do it at school all day. When you transfer the redsnow file make sure you get the extracted app. That's all you need and the iOS 5 software. When you put it in DFU mode the computer will automatically download the apple drivers while in DFU mode.
When you click on extras and select the iOS file it will open up the file from the flash drive since that will be the only place that has the ipsw on the PC.
I have did it all this week at school with no iTunes. You know how school you can't download and install.