Hello, I need to take a cold air return in the basement to the floor level. One of the options I was considering is to cut the top plate as shown on the image (stud on the left is missing) and cover the space between the joists with sheet metal for the upper part. For the vertical part of the duct, I was going to use the space between the studs and the wallboard. Another option, less preferable, is to connect a flange with an elbow pipe at the top without cutting the stud. Would it be acceptable to use the first option or I have to do it with a flange and an elbow?
Your first option is the way its done. Before you cut out the plate, make sure it's secured in a few spots to the joists to give the wall a bit more strength (it looks like it already is from your picture). I'd also put pieces of drive cleat across the cut out section on both sides of the wall.