Yes, it's tough against Shadow, I added a 3-mana banish with a puppet, but it's not very effective.
I added two 3/3 gold creatures; it's still not great against Shadow, but it's better against Rune. But it's still not a guaranteed counter. Honestly, I don't know how to counter Shadow right now; I used to run an AoE spell for 4 mana, but I've stopped using it again. You struggle and struggle, but it doesn't seem to matter.
I don't play Icarus at all; at one point, I even removed the kittens out of frustration, but then I brought them back because they're too good. I use lions, mechanics, 4/3 golems, they draw cards, and then they discard themselves instead of the cards. I used to play flying swordsmen, then I switched to Hamelins to double the draw from the 3-mana draw creature, but it didn't help much.
Three swordsmen for the general pool (although I might change that too, I need to think about it), lions and mechanics are must-haves, and I don't use golems; I found Radiants to be not so much a win condition as something utilitarian for trading or taking a bite once a year. I tried Graviwife, similar to Icarus – it's a bit better; you can trade away a strong creature, plus it draws random cards, but I've removed it for now.
In short, it varies; you need as much analysis as possible, and you probably need to fabricate what you need at the moment – Radiants, Mystics, or Analyzing.
There are a lot of options, and I often try different things; I haven't found anything super reliable yet.