Tanuki and Reindeers sound alike in Japanese so it's a joke that Chopper is assumed to be a Tanuki
there are money things speaking for that:
Yamato pose as Oden something a Tanuki would do.
Yamato wants to see the scabbards
Yamato has Momo and if Toki or Hiyori is the one of them he should go there
Yamato has a DF but was never shown yet that would speak for something surprising like that
it would fit the chapter titel perefectly.