This is a good question because there is no simple answer. One of the problems is that 'lips' and 'lower/upper lip' refer to different things.
It seems there is broad agreement about what 'lips' means. They almost always refer to the pink part (i.e. what you apply lip balsem or lipstick to).
But there is less agreement about 'lower/upper lip'. The accepted definition is that these words refer to both the pink and the skin-colored part. This is different from what 'lips' means, so that obviously leads to confusion. A lot of people use 'upper/lower lip' to refer to just the pink part.
So, we've been talking about 'just the pink part' and 'both the pink part and the skin-colored part'. What about 'just the skin-colored part'? Well, in colloquial English, there is no dedicated word for that. (Some people will answer 'philtrum', but as you have already indicated, this is wrong because it only refers to the part between the ridges in the center.)
But we still need a word, so we can just use a medical/scientific term to refer to "the skin-colored part of the lip". This leads to the often used term cutaneous lip.
Here's a summary of the correct names.
- The lips usually refer to just the pink parts.
- The upper lip is everything between the mouth opening and the base of the nose.
- The lower lip is everything between the mouth opening and the chin.
- The vermilion zone is the pink, non-wet part of the lips.
- The cutaneous lip is the skin-colored part of the lips.
So the best answer to the original question would be cutaneous upper lip.