To my knowledge, there is nothing that a patient can do to prevent neutropenia.
I don't believe that there is evidence that exercise helps prevent neuropathy, exercise surely can't hurt. I walked throughout my treatment - some days less, some days more - that keeps blood circulating in your feet. I didn't experience any neuropathy in my feet.
I am a free lance writer, and I type on the computer all of the time. I had very little neuropathy in my hands. I wore gloves religiously to help keep my hands warm, and I messaged my hands all of the time.
Of course, this advice is anecdotal, but I was fortunate and suffered no long lasting neuropathy.