'Floating voltage' on the tip doesn't matter as long as you are only working on cables that aren't connected to any electronics, or are working on a device that's isolated on your bench with absolutely no external connections to it. However if you work on anything that's ground referenced, or has a power lead plugged in, even though its switched off at the socket, you risk zapping it. e.g. CMOS analog switches commonly used in consumer AV equipment for input selection are notably sensitive to ESD and leakage current damage.
It would be easy enough to mod that PSU to resolve the issues. Its got pads for a fuse, so just cut and peel off the 'fuse' track and fit a suitable wire ended fuse. The leakage current through the Y capacitor to the floating output can be resolved one of two ways - ground the output, or add a cap of 10x the Y cap value in series with Y cap on the output side, and ground the junction of the new cap and the Y cap. In all cases the added ground wire should be insulated, and sleeved where it crosses the primary side circuit.