You need to decide, even if not strictly to the rule box, you may feel minimum risk anyway as no where near bath or shower, and will not be using a shaver while socking wet. There is no rule for hand wash basins, but I realised in my bathroom a shaver would be safe, as held in my hand in use, but a tooth brush on charge would not be safe, as all too easy to knock whole lot into the sink.
The whole idea of the isolation transformer and the IT supply is touching an earthed item and the faulty appliance at the same time is unlikely to give you a shock, you need to touch both lives to get a shock, which is unlikely, there is no neutral at a shaver socket, just two lives.
The problem with the IT system is once it supplies more than one item, you can have multi-faults, so only safe with one item, specially as there is no RCD protection with a shaver socket, but whole output limited to 300 mA.
Personally I would return it as unfit for purpose, but I have some items I know don't comply, I have a few of these

which do not comply, but in my bedroom plugged into an extension lead, so fused by the extension lead fuse, they are handy to use switch mode power supplies with 100 - 250 volt input and USA plug formation. I have no children in the house, and visitors will not have access to my bedroom, in fact to allow them access could be deemed illegal as I have transmitting devices which require a licence to use.
So although if found at work I would smash with a hammer and put in bin, at home I feel safe in my hands. But they came with equipment and the suppliers were technically breaking UK law by including them with the equipment. But suites my needs.