How Does a Volatility Skew Affect the Delta of OTM Put Options?

A volatility skew increases the magnitude of the Delta of OTM put options (makes it more negative). Since the skew implies a higher implied volatility for OTM puts, this higher IV increases the perceived probability of the OTM put expiring ITM.

As Delta is a measure of this probability, the higher IV pushes the OTM put Delta further away from 0 and closer to -1.0.