I believe you can change hair with the mirror you can make with the cute workbench.Operating table is unfortunately limited.
It can do eye type/color (iris and sclera both), ear type, nose type, boob size, skin tone, nipple tone, and can color only 1 of the 3 sections of hair.
Can't do all the hair color, or it's style. Can't adjust the size of anything other than boobs. Can't add/remove futa status. Etc.