Our situation was similar – good local comprehensives but also a couple of really top notch super-selective grammars. We just did home prep – I am not a teacher but I did my research (the 11 plus forum is massively helpful: www.elevenplusexams.co.uk/forum/11plus/index.php) and if your child is happy to work with you there is no need to hire a tutor for the CEM or GL 11 plus tests.
In our area, only about 1/3 of the class sat the test, and I don’t think many had tutors. In a nearby, more affluent area, most of the class had a tutor from the start of Y4, and it was all very stressful, with lots of borderline scores and plenty of secrecy. I can’t see that the huge expenditure and stress on those kids made much difference: it was still the brightest kids that got in.
If you think you can work effectively at home with your DS, you should be able to keep it quite low stress. In Y4 the main thing to do is to make sure he’s on top of all the learning at school, fluent with his times tables and is reading a variety of books (including out loud) and is exploring any new vocab. On top of that, you could find a couple of short slots per week to sit with him and look at some ‘picture puzzles’ (non-verbal reasoning questions) and perhaps some online maths games (nrich and maths playground.)
As a trained teacher, you will be in a much better position than I was to help your child, but honestly, looking back, I relished the challenge of learning what it was all about, and carrying the pressure myself, to keep it quite low-key for my daughter.