Regardless of the method Okabe uses, does it seriously matter how he got his handphone?
I would even say logically, the way Okabe approached Moeka right from the start was too dangerous for the following reasons:
1) Suzuha never managed to subdue Moeka on any of her attempts of assasination despite her skills. This would more or less give Okabe some knowledge on her ability when it comes to combat.
2) Okabe himself has been shown to be weak when it comes to stamina(due to lack of exercise)
3) Combining these 2 reasons, it would be a bad idea to go alone into Moeka's house, without knowledge on the chance of her having any backup nearby.
4) Making it worse, he did not bring any self defense weapon with him.(High possibility of Moeka having a gun and at least Okabe brought a fake gun with him when he tried to meet Moeka alone the last time)
With these reasons, I would say that Okabe did not give much thought on how he would approach Moeka, and when he got into a fight with Moeka, I doubt he would even give a second thought in the middle of the struggle of what would happen to her if he punched her instead subduing her.
Also, Moeka's death is more or less certain, so there's no point in talking about the consequences of any methods.