Mount Ishiwari Hike Footwear?

Solo trip in early November, hoping to hike up Mount Ishiwari then down through Mt Hirao & Ohira. Is this doable in a pair of Skechers or Asics, or are hiking boots a necessity? A video recommending Ishiwari as a day trip recommened 'grippy boots'.

My planned footwear for the trip are my Dr Martens (always walking long distances in these, so comfort not an issue, and they zip up the side, so easy to take off), and a pair of runners.

Do I need to add hiking boots? I'm a size 10 in UK sizes – 10.5 US – and I've heard that buying my size in Japan might be hit & miss.

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