With care, the covers can be removed and the needle reset to zero. It's likely that vibration has loosened the needle and once set, a gentle push will 'secure' it again. I've managed to take apart the later Breva clocks (with chrome surround), to clean up the internals.The chrome one is trickier, AFAIK, due to internal plastic clips and the cursory look that I made of a purchased all black one, suggests that your clocks will be easier.
If you have no windscreen, then it's a quick enough task but go carefully.