I am not a tax expert, but I can tell you that "NO", you do not have to file this in a schedule D. It appeared as income, and was taxed as income, so it gets filed as income. I have been filling out long form for four years. I have 401K, and tuition reimbersment. The tuition reimbersment works much the same as your unequalified company stocks and I never needed to file a schedule D. But like always, this should be something that your tax-preparer knows! There maybe other things that he/she does not know in which you could benefit directly. My suggestion would be to go to an accountant at least once to see what they can do for you. Besides, tax laws are always changing, and they "must" know them because their job depends on it.
Hope this helps.