When using Ikelite strobes with my underwater cameras and housings, I routinely set my white balance to the "K" or Kelvin setting and specify a colour temperature of 4800 degrees.
Unfortunately, that assumes that Ikelite have correctly measured and reported the colour temperature of their strobes and that there is no variation between the strobes themselves. My results below, suggest that while the DS161 is rated at 4800K, it has a somewhat higher colour temperature.
I shot my Nikon D2x with DS200 strobes for years and got very close to perfect white balance every time, especially with macro.
How did you verify your white balance was "very close to perfect"?
An accurate way is with a 18% gray card. And an even more accurate way would be to use a colour checker, but that is very fiddly.
I regularly use a Kodak 18% gray card for setting and verifying my white balance settings.
As an experiment, I set up my D7000 using instructions you posted - so that the white balance would be set to 4760K. I then connected my D7000 to my 2 DS161 strobes and took a photograph of the gray card. Just for fun, I also took photos of the gray card with the camera set to "Daylight" and "Flash". I imported the photographs into Lightroom for analysis.
The development module in Lightroom provides both a histogram and point analysis of the photo. Additionally, there's a "dropper" which will set the white balance of the photograph so that red, green and blue are the same levels.
The photo shot with white balance set to 4760K had a distinct blue to it. Lightroom shows the colour temperature as 4750K with a Tint of +12. The histogram showed that blue was brighter and separate from the red and green channels. Using the point analysis, red and green are around 38% (with green being slightly higher than red). The blue channel was over 42%. If I use the white balance dropper, to set the white balance, it sets the Temp to between 5200 and 5250K with a tint of +3 to +5.
The "daylight" shot looks much more neutral. Lightroom also shows the Temp as 5200K and the Tint as +11. The histogram shows all three channels almost together, with blue slightly higher than red and red slightly higher than green. The dropper shows numbers like: R: 42.4 G: 41.8 B: 43.0%. Using the WB dropper makes little difference either leaving the Temp at 5200K or changing it to 5250K. The tint drops to +3 to +5 and this would be expected.
The "flash" shot was wrong and obviously so. Lightroom shows the Temp as 6600K and Tint as +10. The histogram show more separation than the other two with blue being the lowest and and red the highest. Point analysis is like R: 47.7 G: 44.9 B: 41.9.
So, at least for my D7000 and DS161 strobes, "daylight" was the closest.
If you want to set the white balance in the camera, a more accurate way would be to use Preset manual (Page 123 in the D7000 manual) with a gray card and using the strobes as a light source. However, if the camera is not used exclusively for underwater photography with the same strobes, it is far easy to just shoot raw and set the white balance in post processing. The problem if you use the camera for other photography is forgetting to set the white balance before underwater use and so it is wrong anyway.
I do a lot of different photography, but most of the time I'm using a strobe of one sort or another and with different soft boxes. I have a number of white balance presets in Lightroom created by photographing the gray card with each of the different combinations of strobes and diffusers I use. It is just a matter of selecting the correct preset on import (or even later if I forget). I even have the luxury of creating a preset after the fact (postset?).