I've had this electric space heater for probably about twenty years. Its one of those long and thin ones that does not have a fan. It is a convectron by slant fin model cve 1500. The plug is two prong and from what I can see completely made of metal (except for the cord and knob). I use it everyday in my finished basement and it has served me well. I'm not worried about fire since I'm always right there but I am concerned about electric shock. Am I underestimating my risk? Am I overestimating it?
Twenty years is not that old really. This will be a double-insulated appliance so grounding is not required. The male plug is probably polarized so keeping the correct polarity should be ensured. These things should keep the appliance from shocking anyone as long as everything is in sound condition.
It's probably well insulated on the inside to the point that the code at the time allowed a non-grounded plug.
However if you are really worried then put a GFCI plug on it. It will protect you from shocks by shutting down the power if a fault in the wiring would send current to the ground (possibly through you).