Green’s Dictionary of Slang

skyscrape v.

[sky-scraper n.1 (1)]

to raise one’s hat in an exaggerated manner.

[UK]R.S. Surtees Young Tom Hall (1926) 155: Replacing his cap on his grizzly head, after the sky-scraping he gave it as his lordship cantered up.
[UK]R.S. Surtees Young Tom Hall (1926) 279: How he sky-scraped and bowed and bent forwrd to the raisings and touchings of hats.