If you are talking about 'assassination' missions, for example a pirate lord, deserter or terrorist, then no, you do not need an interdictor. You will be pointed at a target system, when you go to that system you either scan the nav beacon or honk a discovery scanner and you will be given a location where you can find your target (planet x). Go to that body, get close, within the million meters range rather than Ls, and at some point a mission specific USS will appear. It will be announced by your ship's computer and will have blue text. No need to look at other USS. Drop into the USS and your target will be there. You can use an interdictor if you want as the target should also spawn in SC within the window of opportunity given in the mission description.
If you are referring to kill x pirates from a specific faction, then I believe an interdictor is a good thing to have, as while the mission tells you to find them at RES or nav beacons, not enough spawn.