First of all an answer to the main question - no, as far as I'm aware there is no 'requirement' from ICAO for trainers to be in any way approved or endorsed.
Does anyone know if there are any ICAO requirements for SMS training to be delivered by an approved/trained SMS Trainor/Instructor or can anyone who has received SMS training go back to their respective organisations and produce an internal training course and deliver it to their organisation - should the person delivering attend (or indeed is it mandatory) to do a 'train the trainer' type of course.
But do you mean training
about the SMS or training in the competences and skills that are needed to perform tasks required by the SMS. The two are rather different!
As one auditor story goes, the best way to determine how healthy a company's SMS is, is to walk around the company and casually ask non-descript people (for example, hangar cleaners, accounting staff, security guards, etc.) if they know about the company's SMS and what they think of it. The quality of responses from various people in the company will at least show how effective the SMS training is.
There is a view that hangar cleaners or, indeed, those in many other roles in an organisation, do not necessarily need to know very much about the SMS at all - what is important is that they know what their responsibilities are and do what is expected of them.