Whoa, stop right there - you've said negatives but this looks like a print. Are all the photos printed on paper like this? Then you can't do with prints what can be done with negatives. Prints are on paper.
Don't get water on a print, at all, keep it dry.
I don't know what soap may do but water will ruin the finish/the surface. But since these would have been done on light senstive photo paper and developed in photo chemistry, the darkened parts of the images are more or less permanent. They could fade in time but the image should mostly still be there and won't just rinse off.
I haven't tried yet with old family photos but with my own B&W darkroom prints if just the surface (shiny part) got wet and damaged, I'd run it thru fixer (not water, liquid fixer); that will restore the gloss. But it would be a matter of if I'd want to try it with an older photograph or leave well enough alone. And you'd have to know how to 'fix' and squeegee prints, etc. This would be for 'modern' photos that used photo paper & fixer comparable to what is still used today, which could include the era of that car. There were other photo processes like tintypes that I wouldn't attempt running them thru fixer like I've done with prints on photo paper.
This one looks fairly deteriorated but usable. Usually in restoration I think as little as necessary is done. I'd think about putting it behind a mat with an oval opening so you can see the cool car and them sitting in it, and not so much of the background where there's more deterioration. Or maybe a standard rectangular mat if you could place the photo to show mostly them in the car with the house and keep the roof and trees behind the mat. The good thing is the part of the photo with them seems in better shape than the trees, etc. in the background.
Other than a blower to blow off dust, or maybe a very very very soft brush intended for this purpose, I'm not sure what else you can do. Of course you could scan them and make adjustments in photoshop (or whatever) to the digital copies and then reprint them for display.
This one is certainly salvageable and not the worst I've seen. To me they're vintage and part of the history of the photos is the worn, faded look that gives the feel of the time period in photos taken long ago.