1. What you would have is a weight that contains Murano canes. But it is only deceit that turns it into a "Murano weight".
2. Yes, a sticker stating "Murano" could be made (and they are already available - real or not).
3. The question about not focusing on just canes is very pertinent. It is always best to examine all aspects of any item before deciding on its likely place of manufacture. But cane details always have a good story to tell and are, in my view, one of the most important aspects for attempting to identify an unsigned / unlabelled weight.
However, we should put all this in context. Canes have, since they were first made, been used by other makers. For example, canes by Bussolin (1830s Murano) were used by Pietro Bigaglia (the person usually credited with making the first of what we now call a glass paperweight). In more recent times, cane making has been "outsourced" by companies who did not have the resources or skills to make canes themsleves. And in the years between, around the world, all sorts of exchanges of canes have been made.