I assume that "skill remover" means "ability remover" and not "activity canceller". With this given...
I wouldn't cancel the activity in the first place.
You will produce this wonderful discrepancy where climbers cancel, shimmiers keep doing what they do merely because of nonpermanence of a much-earlier skill assignment, and sliders again cancel.
All four options feel awkward: Ditch interesting gadget idea over this, make gadget but not have it cancel, make activity-cancelling gadget and turn lemming, make activity-cancelling gadget and face the wall.
If the choice is purely between cancel and turn, or cancel and not turn, hmmm... I feel like it's more natural to make the gadget non-turning, leading to falling lemmings that face the wall, always. But still unnatural.
What are the cases where we turn? How natural is the turning to the design?
Let's go back to the roots: Why is there turning at all in the climb activity? Climbers that hit ceiling turn. Ceil-hitters
must turn because the skill's design doesn't work at all otherwise: Non-turning ceil-hitters would re-climb the wall over and over. Thus the turning is already
tacked-on. necessarily part of at least one transition.
The exact same reason applies to exhaustion. The exhausted climber
must turn, otherwise the gimmick design doesn't work and he would re-climb eternally.
Jumpers assigned to climbing lemmings make them turn and then jump from the wall; this design is unnatural in the first place, why can you even assign jumpers to climbers. That's a grotesque break from the assignment rules.
An argument for turning cancelling that doesn't depend on transitions: Nowhere else in the game do you produce falling facing the wall. You always fall facing away from the wall.
Another argument for turning: Since the pin of NL is in the wall during climbing, which is terrible leftover from L1 but, well, you're stuck with it, you would move the lemming backwards to have it fall. Nowhere in the game do lemmings move backwards. They always turn first and then move forwards.
That leaves us to look at the cases where the lemming already doesn't turn. Hoisting obviously, but we aren't near the top, so that shouldn't weigh too much.
Assume we assign exploder to the climber or shimmier. Which direction does an ohnoer face? I suppose they face the wall? Of course it doesn't matter much, but it's one of the few things that come close to what we want to decide.
Very close is also the vanishing of the wall while we're climbing/sliding. The climber will think that he's at the top and hoist, but that's leftover cruft from Lemmings 1 when they didn't consider much that you can do all kinds of weird things to the terrain. What does the slider do when another effect suddenly removes the wall?
Yeah, vanishing wall seems like the closest scenario, and I think I would expect the gadget to behave like that. Everybody face the wall after cancelling. There is no need in the design to turn, unlike for the ceil-hitting. Let's see if I still think this after sleeping over it.
-- Simon