Dexterous manipulation, especially of small daily objects, continues to pose complex challenges in robotics. This paper introduces the DenseTact-Mini, an optical tactile sensor with a soft, rounded, smooth gel surface and compact design equipped with a synthetic fingernail. We propose three distinct grasping strategies: tap grasping using adhesion forces such as electrostatic and van der Waals, fingernail grasping leveraging rolling/sliding contact between the object and fingernail, and fingertip grasping with two soft fingertips. Through comprehensive evaluations, the DenseTact-Mini demonstrates a lifting success rate exceeding 90.2% when grasping various objects, including items such as 1mm basil seeds, thin paperclips, and items larger than 15mm such as bearings. This work demonstrates the potential of soft optical tactile sensors for dexterous manipulation and grasping.