River's sonic doesn't appear to be built over an existing sonic screwdriver and has many differences to the original prop. However, it shares the same basic shape, size and some details (like the crackle paint).
I'm no expert on the prop or the ins and outs of its creation. However, using some of the tools I have...
Here is a shot from Nick Robatto's Facebook, showing some of the CO toys, Wand Co. sonics, screen used props and some of his creations side by side.
You can see how similar the CO toy is in size to the Robatto replica (he made the original, BTW). It's not quite 100% exact, but it's pretty dang close.
Here is my River Song toy next to the Wand Co. 10th sonic, which we know is exact.
It matches very, very well. The main body (not the cap or emitter) are almost the exact same length. The ridges match up perfectly (though the shape is different on River's).
How do we know 11 didn't repurpose the shell of his burnt out sonic? We don't. He may have used it so 10 would recognize the device (we have seen numerous other sonic devices in the series, and are about to see a few more next season).
It has a big neural relay hidden inside that the Doctor has no use for. The screwdriver appears to be built around that. Why would he build his own sonic around a neural relay then use it for hundreds of years? (btw, 11 has used his sonic for 300-ish years and it doesn't look beat up at all)
We assume it's ancient due to the weathering, but: TIME MACHINE. And we do not know how long River had it between that night and the Library. We assume it's relatively close to the library expedition, but we don't know. We can also assume River could have a long lifespan similar to a Time Lord, and may have lived 200 years between "Last Night" and "Silence in the Library." (though I seem to remember her saying she ages normally... I don't recall)
And to throw a curve ball into the mix, who's to say the cyborg 47th Doctor didn't come back in her battle-SIDRAT and throw it at the 11th Doctor and say, "use this to save the pretty lady with the 'fro."
All this talk about continuity being screwed up and things not making any sense are caused by one thing: lack of imagination.
EDIT; Anyway, yes. You can theoretically use the Wand Co. sonic as a base, but the ridges are different and the Future version is a bit thicker. River's doesn't extend, the end cap is different, the emitter is a little different and the emitter lens is different. The activation switch is in a different place and, if you want to keep the remote or sounds, you wouldn't be able to add a neural relay inside.