I know these Dell motherboards: The front header IS NOT THE PROBLEM and can be easily wired in. THE PROBLEM IS that the CPU heatsink is secured by a black plastic frame with one clip on each side (with green locks on top) in which is secured by special standoffs/holes in the motherboard tray which the black plastic frame gets screwed into - this is where any aftermarket computer case will not have those standoff holes. Maybe the right shortened screws with nuts might work but without a backplate one takes the risk of damaging that motherboard from tightening. The holes for that heatsink retention are not standard so no aftermarket CPU cooler would work on that as well as that Case fan has to be used otherwise the Dell Bios will "burp" on you. In short you'd have to find a way to secure the CPU heatsink rentention, must use the case fan and might have to somehow cable tie another fan to the heatsink due to the loss of the green shroud.
Another thing all: That is a Matx motherboard and NOT BTX.
Yes Dell made computers with BTX motherboards but the OP's one isn't one of them.
The OP either has a Dimension 2400, 3000, B110, 4600 or 4700 which are all Matx motherboards and the difference is that the 4700 has a 4 pin case fan as the others have 3 pin with a unique plug but all of them are proprietary and need to be plugged into the Dell motherboard.
There are a very very few aftermarket replacement fans that can be surgically altered to make it work.