Okay, so I'm moving the ligature topic away from Vilem's Mac Installer one (https://forum.colemak.com/viewtopic.php?id=274&p=2) so we don't clutter that topic up with relatively unrelated stuff.
Okay, here are some of my attempts:
I realized that Shai wants a capitalized 'Cmk' and not a 'cmk' as the official abbreviation. Some of my attempts at making a ligature logo (base) were made before that, but I think the final version will have to be capitalized.
Font: Sans(?). Middle one: I tightened the gap in the 'c' for graphical effect; works well I think. Right-hand one: Not too happy with the capitalized version - but this one isn't quite geometrically correct either. The joining of the 'C' and the 'm' is a mess, but it could probably be done better. I'm leaving this one for now.
Font: VAG Round; lots of fun with this famous "Web 2.0"-ish font. I tried removing the 'k' stem, and I rather like that left-hand one graphically. Then I realized that the 'm' can be hard to distinguish from an 'n', and tried to do something about it. The result may be a bit whimsical - not sure. It's a bit hard to make the capital 'C' and the 'm' play nice. That right-hand one is both weird and hard to get so I'm not too pleased with it.
Font: VAG Round. The right-hand ones are condensed to a 4:3 aspect ratio which I think may work well on an icon. Not bad, actually - even if I had to let go of ligating the 'C' to the rest. The right-hand one is rather good I think, with a 'k' stem adjusted to be of the same height as the 'C'.
Font: VAG Round. On Korivak's suggestion, I tried re-ligating the 'C' and since I couldn't risk it turning into a 'G' I lopped off a bit of 'm'. Instead of condensing to 4:3, this compact icon went all the way to 1:1 which is striking I think. I'm quite pleased with it, but I'm unsure as to how well it scales.
[Edit: To the right are two stroked versions, as suggested by Korivak. Not quite pleased though - the font shape doesn't take tweaking well. I'd be better off using a thinner VAG Rounded... but I don't have one I'm afraid.]