I have some idea, but the situation is complex. As I understand it, there’s essentially no specific legislative requirement for PAT testing under any circumstances. Testing is carried out by people who believe that doing so will help them demonstrate, should the need arise, that they took all reasonable measures to make sure that equipment was safe, because ensuring safety is what they are actually obliged to do. If an offence has been committed then that will be because the kit will have turned out to have actually been unsafe. There is no specific offence of kit not having been tested.
I started to write a long spiel about the Electrical Equipment (Safety) Regulations 2016 and the relevant standards that apply under those regs. Then I stopped. The fact is that no-one behind a shop counter should need to become an expert in that. Mick’s charity will have insurers who will cover them if there is a claim made that the kit they’ve sold has harmed someone. They will also (I imagine) have a lawyer who will stick up for them if Trading Standards turn up on their doorstep accusing them of selling unsafe electrical kit. As I understand it those are the only two things which, in the real world, might go wrong. In return for covering you and sticking up for you, the insurers and the lawyer should be able to tell you how they expect you to behave. That might, or might not, include expecting you to PAT test the kit that you sell. The only way to find out whether it does is to ask them. Better still might be to write to them saying what you plan to do and asking them to let you know if they’re not happy with it.
If the person at the charity who will be responsible for doing the testing doesn’t have a consumer electronics background, and a familiarity with at least the basics of the safety testing, then I imagine it would be a very good idea to send them on some sort of PAT testing training course. There are plenty out there to choose from. The more you pay, the more you should learn, and the more impressive should be the certificate that you leave with. But I think anyone can set themselves up as a PAT testing trainer. That’s one reason why there’s such a wide range of confusing advice out there. Quite a few such trainers are stating that what are in fact just their personal views are somehow formal/legal ‘rules’ or ‘requirements’. Safety professionals have been arguing for decades that PAT testers’ standards are not consistent, and are sometimes demonstrably wrong. But in the end that just comes down to the quality of their training and, if they’re working for a business, their management.
As far as the specific question of second-hand PAT testing equipment goes, I wouldn’t have a problem with using a second-hand tester as long as I was confident that it was working properly. I believe quite a few of the manufacturers offer testing and calibration services for their kit and that would be one way of establishing confidence. Another would be to take it along to whatever training course you go on and getting the people who run the course to OK it. If they can’t do that then I’d start to worry about their competence. Yet another would be to test/calibrate it yourself. The tests it carries out are pretty simple. It wouldn’t be very hard to mock up a ‘faulty’ item then to use your tester on it and confirm that the tester detected the ‘fault’ correctly.