The remover already does more than merely cancel abilities and activities: It pries lemmings horizontally out of the wall. Climbers have the pin inside the wall; this matters for oh-noers who don't fall. If the cancelled climber shall fall facing the wall, you must pry it horizontally out of the wall first to not have it walk and turn inside the wall.
Icho recommends firmly that removing the climbing ability should immediately cancel the climbing activity. Reason: The lemming has forgotten how to climb, and we shouldn't care if the game code tests that knowledge mid-climb or not. I'm not as dead set on activity cancelling, but there is good substance to Icho's argument.
-- Simon