を契機に・を皮切りに: the difference
を契機にN2
Meaning
Lead to, As a good opportunity to, As a result of, As a trigger
Past papers
Example
子供の独立を契機に家を改造することにした。
As a result of my children becoming independent, I decided to remodel the house.
を皮切りにN1
Meaning
Beginning of, Starting with
Past papers
Tested once in past papers
Example
駅前店の開店を皮切りとして、そのチェーンは次々と新しい店を出している。
Starting with the opening of the station-front branch, the chain has been opening new shops one after another.
How to tell them apart
「をはじめ（として）」 names a representative item, and the rest are others of the same group: 「富士山をはじめ」.
「を契機に」 means 'using this as a turning point' for a new change.
「を皮切りに」 is the first of a series that then spreads wave after wave; it stresses continuity and spread.