You can hit missiles with your aerials when offstage (with Lucina, Uair, Fair, and Bair). Doing this does not explode the missile; rather, it will clash with it and disable the hitboxes for long enough for you to go through (until he loops it around). Mix this up with airdodging, especially if you can airdodge to the ledge as you will snap to it (I believe that there are vulnerable frames, more than a normal ledgesnap, in this animation so mix it up as he can start covering this option). Finally, conserving your double jump may allow you to jump over the missile, hopefully to the ledge to gain invincibility so he doesn't loop it into you.
Also, as far as using a counter against Nikita, in a situation where you are on the stage I would recommend jumping over the missile and pressuring Snake. He is vulnerable for a little over a second if he is currently navigating the missile when you approach. A smart snake, of course, will drive the missile up in the air and drop control, allowing him to act against you on your approach while covering space, but at this point the missile will have a predictable trajectory.
I don't think the Lucina matchup is too much worse than the Peach matchup, but Peach is probably a stronger meta pick overall.