Akane is probably the culprit.
She fed Nukitani with chocolate(which is bad for people with ulcer) to start his stomach ache, in order for him to leave and privately take medicine(luckily for her, he got a nosebleed that ruined his cutter shirt, which became another reason to leave for a private phone call). That way she can create an opportunity to kill him outside, close to the restroom(where her backpack was placed beforehand). Being his lover, she probably knew of his routines of where he goes when he wants privacy outside the tournament.
Conan might've realized that the culprit(Akane and her chocolate) was the reason to why Nukitani was taking medicine, right before getting killed, here:
The culprit wore the hakama the other way around, compared to how Okita wore it. That's why the blood is in the back:
This could be due to a gender difference, in terms of how you wear a hakama.
Only the chocolate near the edge was melting because only that part was affected by heat:
She might've tucked that side of the chocolate box behind her "tare"(within the "do"), which resulted the extra heat that accumulated on the edge of the box, or/and maybe the sewing scissor was hot and was touching the edge of the chocolate box(while they were in the bag).
The scissor was in someway used as a weapon. Maybe heat played into it. As for blood, the forensics were gonna test for it, but since this was premeditated, she probably managed to avoid leaving blood traces on it. She mentioned toilet paper was running out when she was exiting the restroom, so maybe that played a role again.
Iori is definitely the unknown silent passerby:
Considering that Momiji was willing to do something about Okita, It's possible that she is behind Onimaru's upcoming absence in the finals. She seemed to already be aware of Onimaru's situation, just by getting Iori's confirmation about something. Maybe the Tokyo governor is someone close to her.
And of course, last not but least,... the winner of this Kendo Tournament is: