Based on the photo provided, there's a strong possibility that you can print that model without internal supports. The angle of the walls falls within the limits of just about any FDM/FFF printer. An exception to this would be if you had a structure internal to the cone of the mouth piece which needed support.
ERROR: I neglected to note that your print is created "laying down" rather than vertically. This certainly complicates the printing/support problem. I typically print cylinders without internal support, although it does result in a small amount of droopies within the cylinder. Those are easily cleared away as required and much more easily than a full support forest.
Is it impractical for you to consider to cut the model in half, print both segments, remove the supports more easily, then glue them together?