Andrzejek or Jędruś/Jędrek.
I would say, that family, especially mum would call him Jędruś (it's more childish)
But friends would call him Jędrek.
Andrzejek would call him his good, female, older teacher
Hope this doesn't bloat the overall image
Speaking of old times: I should bear in mind that when referring to somebody, calling for somebody's attention one has to use vocative; especially when we are talking about educated people in 1940's but I think not only. This should be true for everyone about then...
So his friends could use vocative of Jędrek, which is Jędrku ('Jędrku, could you do me a favor?', but 'Where is Jędrek?'). Similar with Jędruś: it's vocative form is Jędrusiu and Andrzejek with vocative Andrzejku.
Hope this will help you to maintain the zeitgeist.
if a german friend from this polish child refers to him and doesn't knows this language differences, it's would be normal that he says always Jedrus to him. Or not?