If your wrist strap-to-ground has a solid 1M of resistance, you're probably not feeling a DC current. But it is possible that you're feeling an induced AC flow. If your soldering iron isn't properly grounded, it could, with just the right conditions, cause an AC feedback loop to form between it, you, and the surrounding environment. Sitting on a rubber mat with wool socks insulates you from earth ground extremely well, so your wrist strap is the only ground potential for the AC to couple to, hence why you feel it only when you have it on. If this is the case, hunting down the source is going to be like chasing a ghost, since doing such seemingly non-important things like moving your chair over an inch might disturb the feedback loop just enough to break it.
Having said that, I would take a closer look at your soldering station and the power supply to make absolutely sure there isn't an intermittent short somewhere, just to be safe. And make sure it's properly grounded. Most of the time these mysterious tingles are due to equipment that has a floating ground while powered by AC.