No, that makes sense. Shimmiers can already be used as surrogate Walkers in this regard, to e.g. cancel constructive and destructive skills. The important part is that neither Shimmiers nor Jumpers should be able to free Blockers - that should remain specifically the Walker's responsibility.
Regarding double-jumping: While obviously this is very common in jump-and-run video games (and then also limited to one double-jump), didn't we rule out Swimmers jumping out of water for this exact same reason? That you can't jump without solid ground under your feet?
If it's possible to jump in mid-air, then it should definitely be possible to jump out of water, because at least there's a surface and some kind of substance there, rather than just... you know... nothing.
I guess the purely game-mechanical explanation would be that you can't assign any other skill to Swimmers either, aside from subtractive (=lethal) and additive ones (=Cloner).
But then again, if you go with a purely game-mechanical explanation, there's no reason why double-jumping should be limited to one repetition. The lemming would jump from mid-air the second time just like he's jumping from mid-air the first time. So this would be inconsistent.
Keep in mind that in most jump-and-run games that allow double-jumping, the second jump is accompanied by a different animation than the first one (usually a flip forwards). The animation for the lemming Jumper, in contrast, would be the same both times. Hence, it would be impossible to tell from the trajectory of the animation alone whether a given lemming is currently performing his first or second jump. And if there's no difference between the first and second jump, then I don't see a way (rules-wise nor coding wise), to make double-jumping possible but e.g. triple-jumping not.
Also, this rabbit hole goes much deeper. If you can jump in mir-air, can you also assign Jumpers to Shimmiers in their Reacher state, then? If our 20th skill becomes the upward Digger, that one would probably also have to include a Reaching animation. Then we'd have Jumper-Jumper, Shimmier-Jumper, and upward Digger-Jumper interactions.