Generally glossy papers will have a deeper black point than matte. The exact ideal depends on the type of printer. If using photographic prints, then it depends on the characteristics of the photo paper itself. If using inkjet based (either die or preferably pigment) then the ink system is also going to matter a lot for having not only deep blacks, but fine detail.

That said, your image honestly does not appear all that difficult to print for a good printer. I don't know much about whitewall, but I could personally print this without issue on my Pixma Pro-1. The image doesn't even have any deep blacks, so paper type probably doesn't matter in this case, just the level of detail in the color that can be produced by the ink system or photographic pigments.

I might actually try it on a matte or luster paper more to go with the feel of the image, which I don't think would look right with glossy due to the highlights from light falling on it. You want something subdued and probably with a nice texture. The traditional problem with matte paper is that you lose deep blacks, but you don't need them here, so it actually makes it easier.