How can I vent a range hood that's not on an exterior wall?
It's unclear from your description, but is there an existing vent you're trying to connect to, which is 10x3.5"?  

You ran 12x3.5" and are trying to connect to that?  The simplest way is to find a reducer to go from 10 to 12". I'm not sure if it's a standard part or not (probably not), but a sheet metal shop (or HVAC) supplier may have it in stock or can make it for you. It's not overly expensive to have them custom make a part like this (in the range of $40 to $100). 

If you can replace the existing duct that would probably be better: the bigger the duct, the higher the airflow and lower the noise. It's also easier to find round reducers, so if the wall cap is round (which many are), then you may be able to just use off-the-shelf parts to do everything.