[QRP] is an ungrounded iron a bad thing?

[KI4YSP]

I'm working my way through an ATS-3 kit with my 15 W soldering iron, but it is ungrounded (two-prong).  My DMM shows ~11 VAC and ~2 VDC between the tip of the iron and house ground.

Do you all think I should be worried about ESD from the iron ruining the components?  If so, can I just run a wire from house ground to the iron to bring down the potential? (That would be how I'd guess grounded irons work, anyway.)  I'd rather not have to go out and buy a new iron.


Thanks folks,
Nick, KI4YSP