Urchin/Merc is crazy good, so unfortunately (if one doesn't like it) a lot of boards require going for it. From a strategy point of view, the simple answer is just "you have to go for Mercenary." The Merc on play effect is incredibly strong the first few times you do it. Trash two cards and probably buy a $5, that's nuts. And of course Urchin's cantripiness, and the Merc trashing means the attacks get played a lot more often, you can be constantly under attack.
Getting Mercenary first is a huge boost, but getting it second usually means you are able to attack longer into the game. In some situations that late attack hurts more. I have lost or nearly lost a lot games by blowing it after getting a huge lead with Merc luck because I didn't account for my opponent attacking me late into the game. It's very easy to green too early once you have a clean Merc deck because you feel way ahead. I would advocate being patient in Mercenary games, take your time and build. This is true of Goons/Militia/Ghost Ship games too.
I don't have any special insights into how to counter it, it's a discard attack so there are the obvious things like draw to X. I think a lot of people forget how good the Lab variants are against discard attacks in general. The best way to beat discarders is to draw your deck. I don't believe much in the fill your deck with ok junk approach to fighting discarders, it's almost always better to try and thin and have 3 really awesome cards in hand.
If you want to ignore Merc entirely, you probably need to wait for a special board: one that doesn't reward deck thinning. Something like Duke maybe.