Proxy app which doesn't requie any root access in android 2.3.6
Simple answer: No.

Long answer:

No, as these app use a native binary installed onto the system to reroute data through the proxy. This is done at kernel level (actually it's done using the terminal commands, but it is done at kernel level), because of this root access is needed.

There are 0 apps that allow you to use a proxy without rooting first. Android 4.x natively supports proxies however.