User blog comment:FutureCyborg18/Toge Toge no Mi's power extended to inert objects?/@comment-3203286-20131115142548/@comment-5900682-20131115143926

Paula is in fact seen holding her pipe previous to the fight, in chapter 190 (click here to see a link to the manga). Also, as stated by Oda, clothes are an exception in order to avoid nudity; however, her pipe is not part of the outfit; it's an object.

She could have indeed put the pipe inside her pocket, but my point is, that there, it would have been crushed when performing  Stinger Hedgehog; one of the spikes sprouted out from her body would have simply pierced through it. My hypothesis is that this pipe, in order to be later seen intact, was deformed into a spike incorporated into the mentioned technique.