How to get rid of this weed (pictures)

[Americanhoney]

I've got these annoying weeds that have sprung up in between my other plants. There are hundreds of these little weeds. Picking each one out is not feasible. But I'm worried that spraying weed killer on such tiny weeds in the beds will damage the other plants nearby, if the liquid weed killer leeches into the soil near the other plants that I want to keep alive. Any tips on a weed killer that won't damage other plants? Thanks in advance.

At this time of year, with warmth and moisture, weed seedlings sprout in their thousands! Either hoe them, which should be done in dry weather, and should eradicate most of them, or if you wish to use weedkiller, use it on needle spray rather than broad spray (most weedkillers have an adjustable nozzle between the two options) I sympathise as I have thousands of my own!

Almost all modern weedkillers are deactivated on contact with the soil, so you can spray the leaves and not worry about it leaching into the soil.

I wait till they're a little bigger, pull them up by hand and then hoe them out.

Thanks for the responses, I'll look into getting a hoe and see how that goes and then try out the weed killer. I'm a bit too impatient to get rid of them to wait for them to get bigger.
We've never had so many tiny weeds spreading across the bed like this and so quickly. It is just spreading from the rear to the front of the garden bed, it is horrible. I dug up some weeds in early spring in the rear bed and every time I pulled them up, small seeds (?) kept jumping out of the plants and spreading everywhere, maybe that has something to do with it.

Hoe

Wolf Garten tools are good, because different sizes of 'head' can be fitted onto handles of different lengths. Some of their 'hoe' type heads are small, to get in amongst plants; others are much larger to cover large areas. They are a bit more expensive than some tools, but worth it because they are very strong and versatile:

www.wolfgarten-tools.co.uk/index.php?route=common/home

Hoes are amazing.
A good hoe once or twice a week will keep the bed agitated.