Pull them up using pliers. It's a lot easier on your hands. Horseherb is pretty tough, you may be able to mow it high without danger of killing it off. How tall are the oak seedlings?

They're from 1 inch up to 6 inches.

Yes, you don't kill the roots by mowing these "volunteers," and they will just come back stronger. I've got a couple of live oaks in my front yard, one near the house, the other closer to the street. The first of these doesn't get any water from the sprinklers, and the ground under it gets little light. It puts out no saplings. I have a well watered raised bed around the other, and saplings are an ongoing problem. I pull them up with oversized pliers, frequently extracting roots up to a foot long. They are highly sensitive to Roundup, and I sometimes give them a squirt of that, when I don't have to worry about killing other plants. This doesn't seem to affect the main tree. Horseherb is said to be impervious to Roundup, so perhaps that would be an option for you.