I once saw two different productions within a fortnight of the same Molière play. One was a close translation of the original text, and it's staging contained many of the elements of the time when it was written. The second one was brought right up into the 21st century, with a modern setting and modern jokes. Quite quirkily it was delivered mainly in rhyming couplets. I slightly preferred the latter though also appreciated the former. I remember this as I try to make my decision now.
I'm currently working on the third book in the Schellberg cycle. This one is almost completely fictional and set in Nazi Germany. I'm allowing my characters to speak in quite modern English. I do agree that this would sound strange if the story were set in 1940s Britain. However we're one step away here as the characters are all speaking another language some of the words and phrases might be useful. In any case, just as in the second version of the Moliere play, bringing our characters into the 21st century might make them more accessible.
A couple of examples:
1. older brother Kurt refers to younger Eberhard as "Bro". This could anyway be a translation of "Bruderchen" or "Mein Bruder" both of which may have been used in the 1940s.
2. A school girl struggling with fractions complains that the work is "doing my head in". This phrase does not exist literally in German. However there was no doubt something equally colloquial then in German as there is probably as well now. The modern German would not be appropriate but the modern English may be acceptable as an equivalent.
So, there seems to be a suggestion that this might work.
However, in the first novel, The House on Schellberg Street , I do use a 1940s' English. This is partly because it is set in that place and time and partly because the letters I transcribed as part of my research produced a certain pleasingly old-fashioned tone.
So. It remains a dilemma for the moment. It could be that by the time you read this a decision has been made.