If you are entitled to the deduction for Business Use of the Home, you should certainly take it. Mailing address has no bearing on your ability to take the deduction. Since you would be filing Form 8829 with a Schedule C (Form 1040), your physical home/business address should be entered on Schedule C, line E.
I assume that you are keeping good business (and personal) records. So long as you have in your possession a copy of the apartment lease, or dated rent receipts showing the location of the apartment that you are living in and from which you operate your business, you can demonstrate to IRS the difference between physical and mailing addresses, should you ever need to.
For more information about the deduction and filing requirements, please refer to:
IRS Pub. 587 Business Use of
Your Home