You should be looking to hand-calc these values, analysis isn't a magic wand to answer questions like this.
Your pump is a fixed component, if you're designing it from scratch that's potentially a very complex challenge if you're 'buying it in' then you can just get it's values off a datasheet.
For sucking the balls through a line your driving values are going to be the permeability of the cotton balls (including the ball to wall seal) and the friction between the ball and the tube, those factors will most likely dominate to a degree that any other details are negligible (on the piping side). Permeability being probably the most driving as for smooth tubing friction will be pretty low, and analysis is unlikely to give you a meaningful value of it, particularly for a natural product.
Also the relative inaccuracies brought in by your design variables will outweigh any inaccuracy you'd gain through only using hand-calcs.