That looks too clean sided a cut to be from another critter, I think your right it's a wire cut. Hydrogen peroxide is never used in deep wounds, and the poster is right that said it's not much recommended anymore.
I have not had great success with the glue idea and so I have turned to suturing those type of wounds. You can order in dissolving sutures from jefferslivestock.com to have on hand if you want, or get some expired from your dentist or doctor. That will not help you today, but an idea for the future if your willing to do suturing.
Leaving the bottom open to drain would be good. Baby aspirin can be given twice a day to help with pain.