it's done "all the time " for contenders-that's why there's that special "nozzle" on the end of some barrels- the 44-40 is kind of like a weak 44 mag/44 spcl, so you just load the same way as you do for 44 mag, but with a LIGHTER powder charge- i should imagine that you use the same shotcup, shot, etc- personally, i've never seen the reason for any of the so-called "rat shot" loadings, as the ball itself is pretty close to lead dust- might be good for rattlesnakes, and short range varmint, but a 22 is far more effective- a novelty at best
other than that, follow what ben said- you don't need the shotcup unless you want it- some people say it gives a tighter group