You absolutely did the right thing, whether you try to reintroduce or not, for the moment things need to settle, and the little one with the bite needs to heal.
Should you decide to put them together again, or just for general info, I have that cage, and for a single it's fantastic, my little Scar Face lives in it, but for a pair it would need some alteration.
Four weeks old is in my opinion very early to allow pups to leave, they have only just been separated from mum, and still have a lot of developing both physically and mentally to do. I like to if possible let them live with their dad or another adult male for an additional two weeks, or if that isn't possible, all boy babies together. Of course if there were only two males, they are paired already, but they will need special attention, diet, set ups til they are seven weeks at least. I keep my boys with dad til they are six weeks, then in the cages they will go to their new owners in for a further two weeks, and only if they are relaxed and settled can they go to their new homes at eight weeks. The current mini poms are seven weeks tomorrow and due to go to their new homes next week, however there is one little boy that has found being away from dad difficult, and is not settling, and displaying signs of stress. Should he not settle that pair will stay a little longer til I know he's happy, relaxed, and ready. For me it's part of good breeding practice.
If you do chose to try them again, and there is of course no guarantee at all that they wish to live together, take out the shelf and the tube, leaving you with just a big tub. Have two identical wheels/spinners, scatter feed, an open nest, or a nest covered with something like a large wooden bridge so it's open at both ends, and a large sand pit. Don't add anything else that can be fought over, and that either can get cornered it/close ended.
That said, they will both be perfectly happy alone, especially in their great set ups you have made them ,and will a lot of fuss from you