I'd say that Bolton cutthroats are perhaps the best match for Stannis...they are hard hitting but vaporize once they meet resistance, which plays hand in hand with Stannis's "when a friendly unit is destroyed" game.
I was thinking this as well. Seems to be a nice cheap unit that hits pretty hard, but also can die pretty easy, which is fine in a Stannis army.
Also, the release of the new Stormcrow units got me thinking that they could supplement Baratheons quite well. The Stormcrow swordsmen are a little faster than wardens, and can hit a little harder with a Lieutenant, but might stick around a little better than the more aggressive Cutthroats. However, as you pointed out, "vaporizing" early may not actually be an issue...
The Stormcrow archers may be even better with the Lieutenant from the other box though, as it lets them fire eight
Sundering dice from 12" away. Any benefits for either unit require the Coin bag (unlike the Cutthroats), but with a 3 NCU list, this should be doable a fair amount of the time. I can see a nice combo where you use Shyra to grab the coin bag, allowing you to then place a free
Vulnerable token on an enemy unit before shooting at it for free with the aforementioned 8 dice thanks to their "motivated by coin" ability. The only downside here, is that a ranged unit doesn't gain many benefits from the Baratheon deck. Or maybe this could be seen as a good thing because you'll have fewer units competing with each other for all of those "when a friendly engaged unit..." cards?
All that said, here's a list I've been looking to build at some point:
Wardens with Stannis
Wardens with Master Warden
Wardens with Master Warden
Stormcrow Archers with Lieutenant
Bolton Cutthroats
Alester
Shyra
Walder
Pros: It's a healthy 8 activations, the archers provide some much needed ranged support without competing with another unit for Coin Bag effects, and those particular NCU's add some welcome control abilities.
Cons/Concerns: The list lacks hitting power outside of card effects, and two out of the 5 combat units are pretty fragile.