From what you described, I would vote for the option of getting him neutered, stay at the vet to board for the first few days, and if it is too much $, let him stay at your friendly co-workers house. My vet charges very little a day for boarding when you leave them with a week’s worth of greens, so it really can be worth it to insure a healthy recovery. You would be investing the same $ in a smaller cage for him to stay at your friend’s house. By the way, that’s also worth it, as a one time cost, because you will be away again over the next decade and will use it repeatedly. (No returns, please.) Might as well get it now. If she has a good place to let him play, like in her bathroom or hall, it’s a good idea to try it this time.
Neighbor kid – No. Maybe in a few years, but not now. She will want to hold and play with him too much.
Roommate: my feeling is, sorry, but if not going to help than you can allow your co-worker access to your home as much as roommate’s friends.
But frankly, this is an ideal time to get that neuter over with under total supervision.