Presumably, Nan is referring here to her hands being stained with the make-up she uses on her face.
On the whole, the use of make-up was frowned upon in the Victorian period, being mainly associated with certain categories of women, such as actresses and prostitutes. However, it did became more popular during Edwardian times; Queen Alexandra, the wife of King Edward Vll, is said to have used it rather lavishly during her later years.
Paint is an old-fashioned term for make-up used on the face; during the Victorian and Edwardian periods, it included various kinds of lip colourings made from carmine, which is produced by crushing insects known as cochineals.
Hot-black is possibly another name for graphite, plumbago or black lead, a soft black/grey greasy substance which could be used in eye make-up (as well as in substances used for blackening grates!). There are also several references in Tipping the Velvet to using spit-black on the eyes; maybe this is the same as hot-black.
Blanc-de-perle was a face powder made originally from crushed pearls but later from other, more poisonous substances; it was sometimes also known as pearl powder, pearl white, bismuthine cream or fard blanc de bismuth.