I've never taken pictures at a car show, so no experience, and my car show advice is very suspect. But I think it is important and very safe to say that the dome diffusers or flash bracket are NOT going to be any answer. The answer is in the purpose of those gadgets.
The dome diffusers work to allow light to go every which way. Intended to be used with bounce flash (aimed up at ceiling, not possible outdoors), but that some light escapes to go to all the room walls (likely no reflective walls outdoors), so that the walls reflect light back from every which direction (thinking to be fill to soften shadows on subject), which normally is Not going to happen even in the living room due to greater distance to walls and back (relative to distance to subject) due to Inverse Square Law (and no walls or ceiling outdoors). You might be able to detect that I'm Not a fan of these diffusers, IMO just a gadget that can be sold, sometimes for outrageous prices. For indoor bounce portraits of people, the
pull out bounce card works much better (primary purpose to add catch lights in subjects eyes, to add sense of being alive in there).
The flash bracket purpose is to always rotate the flash to be directly ABOVE the lens, even (especially) when the camera is rotated sideways to portrait orientation. This flash on the side of lens could make a nasty visible dark shadow on the wall right beside the subject. But when the flash is directly above the lens, this shadow is mostly hidden behind the subject. Which is a great purpose, but pretty limited in use. "Event photographers" walking around Indoors taking pictures of all the guests find it very important.
None of that seems applicable to a car show, especially not outdoors. Serious photography on cars indoors would involve very extensive lighting, very large softboxes, etc.
Outdoors, just walking around in the sunlight, I think direct flash is going to be your only option (forget the domes, they will just reduce the flash power a little). You said shadows were the concern, and outdoors in daylight, you can use Balanced flash, which is Nikons default with TTL flash, called TTL BL flash mode, always used as default (EXCEPT if you select Spot Metering, don't select Spot Metering). Or the SB-910 has a menu to directly select TTL BL mode, same thing, use that in outdoor sunlight (Actually, the purpose of the SB-900 menu is that TTL mode does NOT select TTL BL default, which is often a big plus indoors, But the SB-700 will default to TTL BL.)
In bright ambient light, balanced means the flash level is reduced maybe a couple of EV, to NOT be main illumination, but instead to just fill dark harsh shadows. For pictures of peoples faces in bright sun, it makes a huge difference. For the faces or the cars, when the suns angle make part of the subject very bight, but some of it is turned be in the dark shadow, the TTL BL fill flash illuminates the dark shadow to look more natural, instead of very dark and underexposed. The flash is on the camera, so it lights anything the lens sees, but the Sun is likely at some serious angle to the car (so we are speaking of the Suns shadows). An example of this idea is shown at
https://www.scantips.com/lights/flashbasics4a.html . However that example is using TTL mode and manual flash compensation. TTL BL mode does this automatically, usually rather well.
I suspect your best preparation is to practice a bit on your own car in the driveway, from different angles, including some that include both bright sides and some dark shadows. For illustrative comparison purposes to be sure to understand the difference, include some in both TTL and TTL BL mode with the SB-910 (SB-700 is going to do TTL BL unless Spot Metering). I think composition will be main key, to find the best and most attractive view of the car. Background choice is surely important too. Also practice the TTL BL on peoples face outdoors in bright sun (turned different directions). And if the pictures are for the church, probably a couple showing a larger overall parking lot scene and crowd might be of more interest than all being the individual cars or car grilles, etc.
And of course if you shoot directly into a flat reflective surface (glass or chrome), you will see the reflection of the flash, so pay attention to shoot into angled surfaces to avoid that.