No need to apologize, I'm happy to get your suggestions. For one thing, you've kept me trying. I dug deeper and got out an old piece list for a different WMF pattern (Modell 2200) – no date on the list, unfortunately. The paper is so fragile I try not to handle it, so I didn't get it out earlier, but sure enough, it has a tomato knife (tomatenmesser). However, I only see serrations on the top edge:

Then again, the bottom edge serrations may be so fine they're not showing up in this image. The actual printed image is only 63 mm (2-½ inches) wide, so I've blown it up for this image. The lower serrations barely show up in the Laurel knife image, too.
Yes, from an American perspective, older German place settings have their oddities, especially with regard to size. In fact, Americans are likely to use the place/soup spoons for serving spoons (tablespoons) and the dessert spoons for soup spoons. In this case, I think this knife would be considered a place piece. I don't have a measurement on the knife; I'll have to ask the owner. It may be smaller than a dinner knife; I hadn't thought of that.
Thank you for your help. I'm still not going to give up until I find a Laurel piece list that shows this knife!