This isn't a typical use for Hugin. But you might be able to produce a result by cropping out a narrow vertical strip from each photo and stitching these together.
You can crop the photos by processing them in an image editor, or by adding masks in Hugin.
I wouldn't expect the automatic control point generation to work very well. You will probably have to add manual control points.
To keep all the strips the same size in the Hugin output I would set the output panorama format to 'cylindrical', and optimise only yaw and angle of view for your input photos.
If you do this you may only need one control point between each photo (not forgetting to connect the first and last photo).