It is an interesting dilemma. When the Epicski Academy was operating, students received a questionnaire that attempted to screen their ability, but final assessments were always made on-slope. A skier can be technically proficient and still have areas where improvements are needed, and for that matter, most professional skiers I have known, consider themselves learners most of their careers. Your reply could cover your personal assessment of your technical accomplishments, terrain and conditions, and even cover areas like cornice, chutes and cliff-drops, inverted maneuvers and areas that you still feel you will grow in. If you have a race background, park and pipe or other skills you should mention them. An honest reply of the kind of skiing you do, speed, turns and maneuvers, can help someone identify appropriate equipment that will serve your needs. Discussing your comfort level with varying conditions on specific terrain (they will recognize names off-piste areas of Snowbird, Alta, Brighton, Solitude, Snow Basin, etc.
What equipment parameters would you want? That probably says more than a self assessment.