In your breeder, if you take one corner and replace the farmland with an open wooden trapdoor (placed on the side of the next farmland block), and place a solid block at head height above the trapdoor (so there's a gap of one block), most of the baby villagers will eventually try to walk on the trapdoor and fall down. The adults are too tall to fit under the solid block, so your pair of breeding villagers will stay inside.
From there you can move the babies (who will soon grow to adults) with simple water streams into a separate holding area, and move them out with minecarts to wherever you need them to be (including a fiery death at least seventeen blocks from the player if you don't like their trades, and some kind of trading hall (such as the one Herb_ suggested) for the ones you want to keep).
Some of the babies randomly won't pathfind to the trapdoor before they grow up, so you will still have to periodically cull the herd in the breeder, but this simple setup will save you a lot of effort. You can improve your chances of success by making your breeder floor small (9x9) and putting as many solid blocks (with air above) beyond the trapdoor as you can. This will trick their wandering algorithm into trying to walk on the trapdoor to get to the other solid blocks, and they'll fall down.