I will be frank, you are proposing something that is just beyond the boundaries of sanity.
It is unlikely that signals between the mouse and the dongle are USB compatible, and although technically it is possible to connect the antenna output from the mouse to the Antenna input of the dongle, it is simply not worth it, as you would have to limit the power going into the receiver, in order to avoid "zapping" it.
If you are looking at the conversion because you are tired of replacing batteries on the mouse, but don't want to buy a new one, then a slightly saner thing to do is to take a USB cable, cut off the slave end, and connect the power lines to the empty battery compartment making sure to match the voltage levels delivered by the batteries, and also ensuring that the data lines of the cable are isolated from each other and other parts.
This way you will still use the wireless data transmission, with the "unlimited" power delivered by the USB.
The fact that is is technically possible, doesn't mean that you should do it, and you should only do it if you know what you are doing. Having to fix the computer because you f*k3d up the wiring is much more expensive that a buying a new mouse.
Mice are cheap to buy, and in many cases you can get them for free, from someone that has had computers for a few years.