A hoe requires dry soil but does work well on seedling weeds, but not on perennials - those you have to take out by hand.
Another option you could try is the weed wand, like a blow torch on a stick. You just pass it over the tiny weeds and they will curl up and die. I worry about what happens to any spiders etc on the soil, so I only use mine to clear red mite from the hen houses (OH set fire to one big time this way yesterday
). A weed wand is excellent for pre-emergence weeding for carrots - you need to cover a small area with glass which will bring that patch on by a day or so - as soon as those peep through you can safely go over the rest of the row with the flame, which will kill off the weeds so the carrots emerge the next day to clean soil
Yet another option is covering the soil with weed suppressing fabric then planting through holes in this. This works best with plants started off in pots, and onions and the like. LBS horticulture sell giant rolls for not too great a price.
You will never have a completely weed-free plot so concentrate on where it matters. Onions really object to weeds, for example, but potatoes can cope with more and still produce a good crop. Carrots will be totally swamped, but brassicas don't need perfection.