"is scalping it a bad idea?" Yes!
" Will it harm the grass that I do have?" Yes!
Those grass blades take in sunlight to make nutrients that feed the roots that produce more grass plants, scalping reduces the amount of blade that can pick up sunlight to almost nothing so nutrient manufacturing is stopped.
If the soil is so compacted that aerating is necessary it is too compacted to sow grass seed. Spread the fertilizer either several weeks before seeding or several weeks after.
How much organic matter is in the soil?
How well does the soil drain?
What kind of life is in the soil?
Seeding onto poor soil usually results in poor germination and disappointment. Be sure the soil in a good healthy condition before seeding.

I was only planning on aerating so that I would get good soil contact and have some seeds fall into the holes.
The organic matter is 14.2% tested by Mid West labs.
I have not tested how well the soil drains but what I can tell you is that almost every pull of a Fiskars dandilion puller I get a worm.

I'm really just looking for the best overseeding technique. I guess I was thinking by scalping the grass it would allow the seeds to get sunlight.
What length should I cut it to just before overseeding?

Very few seeds need sunlight to germinate. They do need moisture and too much sun can cause rapid moisture loss which is why most seed companies recommend a mulch after seeding, or sell seed in a mulch material. I would not cut that grass any lower than I normally mow at, about 3 inches.