I (very gently) sprayed regular lysol on very old furniture when I noticed a dusting of weird mold. It didn't hurt the finish on that, but I didn't spray directly on it. The finish on that was several generations of wax..solid wood, not veneer.

Veneer gets ruffly very easily.
Sunshine disinfects. Maybe you could sit it outside to air out and freshen itself?

Diluted Listerine would probably work as a spray for inside the dresser and drawers.
If it was sitting on a cruddy floor, you might like to give the feet and bottom edge a good cleaning while you're at it.