Taʿṭū is an imperfect from ʿ-ṭ-w (ع ط و), here meaning “reaches out” or “extends the hand to take something.” Bi-rakhṣin describes a tender, supple hand or fingers.
Shathn describes thickness or coarseness; ghayri shathn explicitly denies it. The expression first affirms softness with rakhṣ, then rules out an opposite quality with ghayr.
This is positive description reinforced by negative contrast. “Delicate hand” conveys the overall sense but loses part of the precision and emphasis of the two coordinated qualifications.