I spent nearly 22 years working for the National Labor Relations Board, and what I have to say to this young man is some combination of knowledge and personal opinion. During my career, I was reminded again and again that employees regularly overestimated the rights they have on the job. The poster who said you have no right under Federal law to vacation or sick leave is, unfortunately, correct. state laws vary, and the issue is far less clear when an employer has a policy that provides for vacation and/or sick leave but prevents an employee from taking it. If an employee has accrued vacation and/or sick leave when he leaves, there is no Federal law that gives the employee the right to cash it out.
As for my opinion and advice, I vigorously disagree with anyone who would call you a "slacker." You might or might not be a slacker, but it has nothing to do with your desire to take the benefit you are rightly entitled to. For decades, Americans fought for such basic rights as health insurance, vacation, and sick leave. Now, they are considered "slackers" if they take the benefits they are entitled to.I agree with the poster who says you should not take sick leave if you are not sick. When I retired, I had accrued more than a year of sick leave and I got no compensation for it.I felt fortunate I was never sick. Currently, many employers combine sick and vacation time, thus avoiding the problem of employees calling in sick when they are healthy. I think that's a good policy, but if the employer's plan distinguishes sick and vacation leave, I think the employee has no right to call in sick when he's not sick.
My suggestion is to discuss the matter with the professor who runs the lab and see if you can agree on a mutually acceptable time to take the vacation days. If this proves impossible, I would discuss the matter with HR, pointing out the policy to the HR manager. I wish you good luck. Don't feel any need to apologize for the benefits you have earned.