Snuffles is often caused by pasteuerella bacteria, and the standard medicin for that is Baytril. If the Baytril doesn’t help, another bacteria or strain of bacteria may be the culprit and another antibiotic can be tried.
You are right in thinking that separation is bad for bonded bunnies’ health. I don’t think you should separate them for that reason. If Rocko has snuffles, the same bacteria is likely to be present in the nasal cavity of Charlie’s. It’s often like that with pasteurella, lots of rabbits, perhaps even a majority of rabbits, carry it all their lives and it never makes them sick whereas other rabbits do get sick. Why this is isn’t fully understood.
For syringe-feeding a rabbit, I do a bunny burrito, which basically means wrapping the bunny in a towel so he can’t kick out back or claw you etc. It’s of course always best to be two people when force-feeding a bunny, so one can hold the bunny in his lap and the other can insert the syringe in the gap between the front and back teeth (rather a wide gap) and make sure the bunny swallows as you go. You will still spill rather a lot on the bunny and get CC on your clothes, your walls, in your hair etc all depending on how feisty your bun is. But as long as you get something in him, it’s still better than nothing. CC can be mixed with yummy stuff like canned pumpkin (unsweetened), baby food (fruit, berry) or mashed banana, sometimes that entices a bunny to eat it on his own from a plate or spoon.
Other than that, the general rule is to keep the bunny warm, refusal to eat tends to make them hypothermic which is very dangerous. Best thing is of course if Charlie snuggles with him, but you can use a hot-water-bottle wrapped in a blankie or just sit with him in your knee with a blankie around him. You can massage his tummy to help his intestines move since refusal to eat causes the gut to slow and there may be build-up of gas, which you want to get rid of. Here’s a youTube video on tummy massage for a bunny: https://www.youtube.com/watch?v=JnuxGLa2reg
https://www.youtube.com/watch?v=JnuxGLa2reg