How can you detect iron hydroxide or iron sulfide in quarried rocks?
Rocks that turn green and then red seems to me like you might have some copper sulfides, like chalcopyrite (CuFeS2). At first, the copper reacts with the atmosphere to form something like malachite (similar to the green patina observed on things like the Statue of Liberty). Next, the iron oxidises to form iron oxy-hydroxides (as you correctly identified).

In order to detect these things rapidly, you have several options:


Use expensive methods like XRD or XRF. I would recommend against, because these only test the very thing you are analysing, and if you would like to test a whole rock face, this would be extremely expensive. It would however be beneficial to give one of the stained samples to a nearby research institute to test what the material is, either using SEM-EDS or XRD. I might be wrong and it would not actually be copper.
Just look at the rock very close, preferably with a hand-lens. Chalcopyrite (and other copper/iron bearing sulfides) and shiny, usually golden or slightly green-purple when tarnished. You can look at a gallery of chalcopyrite to have a rough idea of how it looks like. Note that the gallery has nice specimens, which yo clearly don't have, but try to see how the lustre and colour look like.
Spray bleach (sodium hypochlorite). This would speed up the reaction, better than acid. Note that this could affect other things in the rock and cause staining or dissolution of things that wouldn't have without the bleach.
Try to smell the rock, especially around the places where you see incipient greening. Can you smell a sulfurous smell? Our noses are surprisingly extremely sensitive to sulfur, and can detect it even when some instruments can't.