A "Specialist Skin Centre" could be staffed by cosmeticians (beauty therapists). In a "Skin Specialist Centre", at least in Australia, you'd probably expect dermatologists (skin specialists). But it might be different in Singapore. Other factors would indicate what sort of place it was (Is there a list of doctors names on the door? Can you see a young girl filing nails in a window?)
"Dermatology Clinic" and "Beautician" would differentiate these two.