No, I am not aware of such software. I think that this idea is hard to implement. You can move the cursor in any given direction at any given moment and expect to see the content of the visible area to be accurately displayed. For that to happen the software must accurately predict where your mouse is going to be at any given moment, else it won't be able to show you the correct content the moment you expect it.
This prediction part is extremely difficult to get right all the time and my guess is that it will require considerable resources from your system to do this. Whatever amount of resources you think you will gain this way, shall pale in comparison with the resources you will be spending on the predicting of mouse movements at any given moment.
Now if you have a Windows machine and want to connect through RDP (Remote Desktop Protocol) to another Windows machine, you can reduce the amount of data being transferred drastically by reducing the amount of colors in the user session you are setting up between machines, disabling Aero on the machine you log into, disable wallpapers and audio on the machine you log into and you can also select a much lower form of connection (56K modem instead of broadband). RDP is quite efficient, but only works between Windows machines.
VNC has also a lot of options to reduce bandwidth, but by design it will practically always consume a bit more as it supports multi-user connections on every user session it creates. RDP is much more limited in this way and will consume less bandwidth because of that.
What do your manipulations entail? Can these be done without a remote connection being open at all? Perhaps it is easier to have a small webserver on the remote machine that serves a custom webpage that allows you to change the things you need. That reduces bandwidth consumption more significantly than any of the above suggestions of reduction above. Such a setup won't require much resources on your end or the remote end, while still having a real-time feel.
