"with skipping" is correct and usable in written English.
You can use it when describing an action that is being performed in a particular way, usually with a sense of joy or excitement. For example: "She ran through the grassy meadow with skipping."
But whether Mr. Perry could get away with skipping a debate is an open question.
Thus, Marina and Bella walk either with exaggerated strides, like students of Monty Python, or with skipping, kicks, and birdlike, stuttering trots.
But when the time came for us to leave the children said, 'we will have a farewell party... with skipping and games and biscuits'".
The piano writing also explores extremes of high and low, with skipping riffs that leap about the keyboard, often getting stuck in the piercing top octave.
McDowell and Jimenez have constantly flirted with skipping back to all square but Harrington and Karlsson look much more comfortable now.
Manny Ramirez is a deeply frustrating employee, the kind whose talents are so prodigious that he gets away with skipping meetings, falling asleep on the job, and fraternizing with the competition.
Established veterans might occasionally get away with skipping an entire preseason, but a second-year quarterback was always going to struggle after losing so much practice time as Robert Griffin III did this year.
Mr. Bloomberg's original defection to the Republican Party had nothing to do with ideology, and everything to do with skipping a crowded Democratic primary and jumping right into the general election in his first race for mayor seven years ago.
Supposedly originated by the natives of Gap (Gavots) in the southeastern French province of Dauphiné, the gavotte was danced in royal ballrooms as a round with skipping steps adapted from the branle.
