Most of the time, Pokemon should be able to pass down egg moves through their own species, and indeed this is the case with Cutiefly. So no, once you have bred Speed Swap onto a Cutiefly, you no longer need the Raichu. If you breed a Cutiefly that knows Speed Swap and the offspring is another Cutiefly, that Cutiefly will know Speed Swap every time. Only one parent has to know Speed Swap for it to be passed down.
It is also worth mentioning here that as of Gen 6, egg moves can be passed down by the mother as well as the father, so if you hatch a female Cutiefly with the move, she can fill the role passing down the egg moves as well. There is no longer any gender restriction, and there is no need to breed the move onto both parents -- I've bred a fair few Pokemon myself recently so I can verify that firsthand.
PokemonDB itself has really good lists of parents for passing down egg moves. You can see Speed Swap on Cutiefly's listing here, and that Raichu, Cutiefly and Ribombee are all potential parents. It does not matter how the move was taught to the parent -- so long as it has a mention on the list, it is a workable parent.