Fingers can detect Nano-Scale Wrinkles; however, larger hands are not more or less sensitive to wrinkles on a flat surface. Even though the hands are bigger, they are not more sensitive. The size may allow a person to feel more wrinkles at once, but will not affect the sensitivity of the hands.
Even though fingers can detect really tiny wrinkles, whether a person with larger hands can detect more wrinkles really depends on the person. Maybe this person is not that in tune with this body and can't tell the difference between silk and cashmere when he runs his hands over both. I don't think the surface area of a finger will have that much affect on how sensitive that finger is to wrinkles.
No, I do not believe that the size of a person's hand determines sensitivity. Anatomy is the same regardless of the size of the body. A smaller person has the same amount of tactile receptors as someone who is larger. This means that a smaller person would be equally able to detect wrinkles than a larger person.
When the overall scale of the hand is larger than normal then the nerve endings at the ends of the fingers will also be corresponding larger and therefore less sensitive to detecting nano-scale wrinkles, which are large molecules embedded onto an otherwise smooth surface. However, the difference between touch sensitivity will be marginal as the nerve endings are only slightly larger.