You caught him in the arcade and attacked him. Shirazu-kun fought and although you stabbed him and hit him on the back of his head you weren't able to kill him at that point, so you went with a plan B. At that point you either disabled Shirazu-kun and kept him in the sauna - which is how I'd say the scarf got involved - or he ran away and stayed in his room, hours later finding the explosive in the sauna.

Judging by the haze I'd say Shirazu-kun died not long before we found him. You made the mechanism with the radio, leaving it on Shirazu-kun and activating it from not too far away. He died, and you went to get rid of the evidence by hiding it in places you thought it wouldn't be found.

That is how it seems to me everything happened.

[There may be holes, though. Mouri connects the dots with the most obvious conclusion, after all]