Guess I'll provide my input as well. Disarmer can go, no questions asked. Sure, disabling traps is cool and all, but honestly this aspect makes the game less like Lemmings to me. I consider the various traps of L1 and ONML are what make the games iconic, even if some of them I'm not a fan of due to how gory some are when killing a Lemming (eg, the icicle trap).
The stacker can go as well, since I kind of consider it lame even if it's a modified version of the L2 one. Even with that aside, there's not much practical uses of it outside of one application that I consider very creative, but I won't spell out what it is since it will otherwise spoil a few levels in level packs. Not to mention that I tend to have a really difficult time with solving levels that provide a lot of stackers. In a way, these are kind of "hard for kaywhyn" levels, though I know several members tend to have similar struggles with the skill.
The rest I'm not as decided on, though I think I honestly can live without the stoner and glider, especially as I haven't found much uses of them in the levels I've made so far. As a matter of fact, I seem to mostly avoid giving floaters/gliders, as well as stoners, though I have more levels with stoners than not. Even then, I kind of consider the floater iconic, particularly since it is one of the classic 8 skills, and I would certainly keep all 8 of them despite not having many "floater" levels myself.
So, this pretty much just leaves 1 skill left to be on the "excluded" list, as well as reduces down to 4 permanent skills. Tough one, but I would probably say it would have to be swimmer AND either one of fencer or laser. Even though I have far more respect for the laser skill now than before once I have actually made levels using it, the main reason I wouldn't keep it is due to how the skill feels too futuristic and hence I feel like it has no place in NL/SuperLemmix. Instead, it should just stay where it came from, L2, though that one is a purely vertical one, not diagonal.
I feel the fencer still has its uses, such as unlimited range/duration as long as there's terrain to destroy or a suitable slope to keep it going, though if you plan to increase the range of the laser then that would favor the removal of the fencer. So, it seems that swimmer would most certainly be excluded for me.
In short, glider, disarmer, stacker, stoner, and swimmer would very likely be my picks, or if not the swimmer then replace with one of either laser or fencer.