At least two falacies on this thread.
"Mechanical Royalties" have nothing to do with public performance. They are paid for use of copyrighted material on recordings (ie. reproduced by "mechanical" means).
Performers are NOT liable for public performance royalties/licensing. It is the responsibility of the "producing body" (ie. the club owner -- or, in your case, the management company who owns the mall). You, as a performer, are not liable for these fees (at least in the U.S.).
I know nothing of Union regs or practices.
In order to use live or recorded music in your business (and performances in the public spaces of a mall would be considered the mall management company using music in their business), you must obtain "Public Performance Clearance" from the owner of the copyrights to that music, or from their designated representative. In the U.S. that would be ASCAP, BMI and/or SESAC. For a single event once -a-year or just occasional things, while single event licenses are available, most venues just blow it off because it is not worth the time or $$ of the P.R.O.s ("Performing Rights Organizations) to persue any legal recourse. For a venue (like a bar or club -- or a mall that has music every weekend), if they don't have the licenses (which range from several hundred to several thousand dollars per year -- depending on how the music is used), they will eventually get sued and they will lose.
If you are performing all originals, then the venue does not need to get anyone's permission but yours (which I assume they have).
DCMaguire
(Former ASCAP licensing enforcement employee)