The choice of preposition has nothing to do with the word parking.
You can only do something at [a] risk, not *on [a] risk. Any of the following would be non-standard with *on in place of at:
- put your family at risk
- it's impossible to predict exactly which cities are at the greatest risk for hurricanes
- becoming a lion tamer at the risk of being eaten by a lion
- as a smoker, she is at high risk of developing lung cancer
- jumping over Springfield Gorge at considerable risk to life and limb
- high blood pressure puts you at risk for a stroke
- he is an at-risk student
- at great risk
- at your own risk
- they remain at substantial risk
The OED puts this use under "of conditioning circumstance", grouping at risk with such other combinations as at great expense, at an advantage, at a disadvantage, and at their peril.
Like many preposition combinations, this is one you'll have to memorize.
In this answer, the * symbol indicates non-standard English.