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I went ahead and did it no supports at the default size for the default Pikachu. I guess it technically printed ok, but yeah with my stock fans there was definitely a bit of drooping inside and around the edges curving up even though it did fit still. I suspect someone with strong enough fans would be able to print this fine without support, but yeah I'll need to for a better result.
Regardless very nice quick hat! It does give him that bit of extra charm making him Detective Pikachu instead of normal Pikachu.