I have a desk job, but haven't taken any time off from work to do this. I don't want to draw attention to it.
Of course, I don't want to tell you how to run your life, but there are those who would say that it is your beliefs regarding the fast ("I can't do...") that prevent you from fasting to completion not your body.
If you are worried about mineral/vitamin depletion you could consider semi breaking fast for a couple of days and drinking only coconut water. That would get you replenished without totally having to start over (though I'm not an expert.)