I think you should get a smaller fan. Nonetheless your airflow won't be terrific with that case because it will be so cramped, but that's usually what you get with a formfactor case. Both cases are the same height, so the black case won't get you any more clearance than the beige case. So I suggest a fan on a small heatsink, I think you can get one for a formfactor PC.
Check this fan out. I did the real math on your space and 3.8 inches X 2.56 cm/in equals 9.72 cm. Divided by 10 to get mm equals 97.2. This fan/heatsink unit is 59 mm tall, which gives you 38.2 mm left for the motherboard and any other clearance. Tell me if this works for you.