Keep the Site Clean
When passing a construction site, there are usually two things that come to mind: That place is so tidy, and those construction workers are so polite!
A green hospital construction site, though, can keep things clean, if not necessarily wolf-whistle-free. For starters, taking care not to trample or drive over or dig up or backhoe or spill paint on existing foliage and squirrels would help. I don't imagine a squirrel painted that particular shade of calming hospital green would find himself particularly soothed.
As the construction project progresses, contractors can recycle or upcycle all the leftover bits of wood, rebar, flooring, drywall -- you name it, if it's in good shape, somebody wants it. There are businesses that specialize in recovering just this kind of non-debris, or there are drop-off sites in many cities where do-it-yourselfers can come buy unused building materials to make their sweet suburban chicken coops.