If I were floating in a void (far away from any galaxy or cluster), would the light from these objects at such distances be enough to see for example, my hand?
Yes, and no. You will be able to see your hand's silhouette as it blocks incoming light from other sources, but you won't be able to see any features on it. For example, illuminance of starlight overcast moonless night sky is quoted at $0.0001\ lux$ which means that in absence of a brighter light source, human eye simply isn't that sensitive to such low illuminance, even if your hand reflected all of the incoming light (it doesn't). What is the minimum lux rating that a human eye can resolve is not as straightforward to answer though, as it varies greatly by specific wavelengths. This is explained in more detail for example in this Human eye sensitivity and photometric quantities (PDF) document, or perhaps Wikipedia on Scotopic vision. But in a nutshell, no, you wouldn't be able to see any features on your hand in outer space, unless closer to a brighter visible wavelength light source. You'll still be able to infer that it's still there and all fingers on it accounted for, though.