[souffle]

This is really common millymollymandy and I would say most hammies living in single sex pairs need separated due to fighting. Sometimes a small stress will tip one over the edge. It is nothing you have done and if you think about it it is not a natural situation for two males to live together anyway.
The rule of thumb is when blood is drawn they need separated. From what you say regarding one being a fatty it is obvious to me that one has been dominant and is bullying the other. You should bathe the wounds once with cooled boiled water and then leave them to heal. Healing takes some time we find, around 2 weeks and then the damaged fur can be a different colour strangely! They rarely cause problems though you should watch out for any signs of infection such as oozing, swelling etc which will need antibiotics.
Keep them separate now. They will likely be a bit put out and confused for up to two weeks but them you will find they settle and they are usually much more people friendly as singles and you will feel much more relaxed with them knowing they will not be fighting.
I hope they do well. I imagine it was just a hormonal fluctuation that tipped one over into attacking the other. Let us know how they go on.