Even a screwed in heatsink would make me nervous... if you have any idea how people in shipping handle packages you'd be hesitant to ship ANYTHING important without heavy precaution. I've had friends at ups and heard from fedex people, and people literally throw boxes around... doesn't matter how many times it says fragile on the box. airports are the same way typically. it all depends on the person handling the box.
for reliability, secure everything within the case... I would buy a mid/mini atx steel comp. Steel because the heavier it is to a certain extent, the less likely it is that someone will throw it. Also aluminum and cheap steels could crush/bend under chance circumstances.
The MB and light pci cards could be left installed along with whatever drives you have securely screwed in. put the HSF and possibly the video card (depending on how heavy it is) in heavy bubblewrap and secure them within the case however you can (duct tape

). you could seal the hsf into the 3x5 bay for instance.
Also, If you are considering transferring the dell parts into another case you'll have to take form factor into account.