I'm trying to achieve a black-on-black design on a business card. See link here: AHC 180 Youth Ministry Business Card. The large black arrow and the grunge splotches are a rich black of 40-40-40-100, and the card background is 0-0-0-95. The card is being printed offset and UV coated, probably via an online printer (I'm ordering them through a third party and don't have access to the printer.) It's important that there be enough contrast between the blacks so that the rich black portions are distinguishable, but I still want the background to have a black/almost black appearance. Would I be better to use some version of a rich gray for the background rather than a 95% (or lower) black? I'm open to all suggestions.
Don't use a black only at 95%.... make 2 different rich black.
One could be 40-40-40-100 and the other 30-30-30-90.
Personally I recommend you use a bit more Cyan in your recipes rather than making all your CMY values equal: if the printer is not well calibrated (or is digital), a black with more cyan will still look steel black and not dark brown (eg. 40-30-30-100 and 35-25-25-90). You don't need to use a 10% difference, 5% more of cyan is enough.
Usually, if you have a 10-15% difference in your black, it will give a nice soft contrast and will not really look gray. 5% is risky and might not be clearly visible; it could work well though if you were using a spot varnish.
With the 2 rich black recipes I suggested you it should look similar to your example.
Also, when you add a lamination or varnish, it can make the colors little bit darker. Not much, but enough to lose some contrast if you use a 5% difference only between your 2 blacks!
I would recommend you go with a deep gray instead of 95% black. If your black arrow and splotches are too subtle, they'll look like a mistake rather than a purposeful design decision. A little more contrast will be more visually appealing and more likely to print well.
Another option is to spec out a spot UV coating, rather than having the entire card UV coated. In the case of a spot coat, you'll be able to highlight your design without having different shades of black.
Remember that 0-0-0-95 is a halftone of black. So I don't think it's what you'd want. At best, you'd want to use a rich gray and a rich black. What specific rich black and rich gray is hard to say as it could depend on the printer.
Note that subtle black-on-black designs are usually done as clear coats such as UV coating or spot color inks (two separate, but solid colors of black)
As for the sample image, that is so subtle that I don't think you're going to get results you are going to be happy with using only CMYK. However, one thing to try would be to use 100% black and a Rich Black. The rich black will be darker than the 100% black in most cases.