To track airflow through a case is easy with smoke or dense fog. To do it perfectly (cleanly) is much harder. Smoke will likely be safe for the electronics in the short-term, but it will stick to things, reducing thermal effectiveness and allowing dust to stick everywhere (look into threads showing the innards of a computer in a smoking household). Fog will not stick to things, but depending on a lot of environmental variables, could condense on the electronics and cause a short, which can destroy what you have.
If you have tons of time, and are willing to make the effort, I think testing with smoke (there might even be guaranteed safe smoke out there for just this thing) will work fine, but you will need to painstakingly clean every component. That means taking everything out of the case, including heatsinks, and bathing them in isopropyl alcohol. Not entirely necessary, but recommended.
Another thing you could do is remove all components from the case, and power the fans in a different way. You will need to simulate the AGP and PCI cards, possibly with cardboard inserts, and the heatsink will need to be somehow mounted, and the fans will need to be powered without a motherboard; but if you can do all that, you might be able to safely observe your airflow.
Know also that you will need a side window or a piece of clear acrylic to replace the side panel, because observing with the side off will not be at all accurate.
Disclaimer: I've never attempted this.