Generally speaking, the answer is no. Giving up a scholarship would not negatively impact your employability when you graduate. As a graduate, the two main elements that would improve your employability are your university results and relevant work experience that you may have gained during your time at university (such as through an internship). Favourable university results (the specific standards can differ between fields) alongside relevant work experience will increase your competitiveness when you apply for positions as a graduate. Of course, further achievements, including scholarships, university academic awards (e.g. dean's merit list, university medal) can help demonstrate your academic achievements and your commitment to your studies, which some employers may consider a plus.
With that being said, giving up a scholarship does not mean you cannot still mention the fact that you were a recipient of that scholarship at some point when applying for jobs as a graduate. In many cases, simply mentioning that you were awarded a scholarship on your résumé/cover letter is enough. You may want to provide proof that you were awarded a scholarship. If that is the case, you can do so when applying for jobs, by including a document such as a letter/email stating that you have been awarded the scholarship as part of your job applications. Many employers allow applicants to submit documents beyond their résumés and cover letters.
I hope this helps!