I hope these wood accent pieces are just an exterior laminate covering and not the structural part of the case. The reason UL and IEC allows PC power supplies and the rest of the PC subsystems (HDD and SSD cables, etc.) to not need fuses is that the box should have a metal interior to stop a cable fire from exiting the box. Having seen a burned up server once made me remember how important that actually is. And to highlight how common this is, we just need to recall that recently in the PC world, there have been video power cables burning due to engineering / manufacturing errors.
So make sure that you keep the smoke in the box, especially if the box really does smoke.
And related: Don't buy things that plug in to an outlet that do not a UL (or ETL) mark on them. The US was the first country to have safe appliances because of UL and similar safety agency standards.