How can I remove a stud to fit a range hood vent?
Options that avoid moving the range or knocking open the wall:

Go for an unvented hood
If there's no top cabinets you could get a ducted hood and run the duct inside the kitchen across the wall then outside where possible.  The choice of hood, size of the duct, and number of bends all have to be to code and planned by someone with more knowledge than me but I hope this can give you some direction if you like the idea.  With some thought this could be made to be not too ugly, e.g. an industrial-look duct, or build a plenum around it.