The fruits should be just fine to eat. Maybe a little less flavorful, but still safe to eat. It does look like powdery mildew, but without seeing a closer up picture, it's hard to say definitively. Here's an article for PW and its removal: http://www
I would have to agree with Joe. It seems that your cucumbers have been affected by common mildew. This will happen when there is prolonged moisture on your vegetables (especially of the squash variety). The mildew is only surface deep so if you scrub them thuroughly it will come off, but the integrity of the cucumber has already been compromised and it might not taste the same as some areas will be denser and some more porous.
Cucumbers also love high humidity (as opposed to tomatoes). They also are not prone to blight (see comment further down by person who thought they were). Completely different plant family so blight hits tomatoes and potatoes.
Looks to me like you thought you had bought a long variety of cucumber, when in actual fact you had bought a round variety of cucumber. Even if the seed packet said different mistakes do happen, so contact the supplier in case other people have made the same complaint.
Mildew can take a whole garden out if not controlled- treat them for blight. Yellow leaves on cucumbers and tomatoes are signs of blight also. Last year blight took out many of my plants. Also stuff grown from hybird seeds are more prone to get blight.
Blight does not affect cucumbers, and blight on both tomatoes and potatoes is seen when dark brown patches appear on the leaves, followed by mould, stems breaking etc. Yellow leaves not a known sign of blight. High humidity and lots of rain a cause.
Cucumbers can get blight-http://homeguides.sfgate.com/treat-cucumber-blight-30388.html, So many different plant diseases....If you have noticed tomato leaf spots and the lower leaves turning yellow, you may have tomato early blight-http://www.gardeni
Sorry I agree in hindsight that cucumbers can get blight, but it is a different strain to tomato blight which only effects solanum crops, (which I don't think cucumbers are, but does include potatoes, aubergine, and members of the nightshade family.)
I agree with mistyhorizon2003, the fungi that cause blight are different species from the fungi that cause powdery mildew. Yellow leaves on cucumber leaves may be a sign of poor nutrition, water stress and powdery mildew. You can't mistake mildew.