Assuming you mean the PSU is connected by a barrel connector, you'd have to run an external ground wire from the station (connects to the tip's ground through the threaded collar DIN connector). You could even place a 1M resistor in series.
Would that cause an issue with the floating PSU
It wouldn't be connected to the PSU at all, so no issues.
Even in the models that include an internal PSU, the ground is essentially pass-through anyway; meaning the PSU itself isn't earth referenced. The aluminum case (assuming it has one), should be grounded for safety, and of course, ground should be connected to the tip through the iron's cable.