Can I use the same kind of tools to sharpen my knives as I do my chisels?
Yes. ~1000 then 5000 is a common progression to get kitchen knives to a good working sharpness. Diamond plates can leave undesirable deep scratches, so I would not recommend someone inexperienced in their use (note that the OP is by his own statement NOT inexperienced) to take them to an expensive knife. 5000 might be slightly too fine for a Wusthoff (depending on the vintage and exact steel/temper used) - if the edge turns out unstable, try to omit the 5000.

By the way, some traditional japanese cooking knives (eg sashimi knives) ARE sharpened in a way very similar to you chisels.