You didn't give any information about what you have tried or much info about your setup. I will assume first that 'steel mesh wrapped around steel rope' is resistance wire around stainless steel mesh simply because this is probably the most used combination.
What I do when I make a coil for a Genisis atomizer is wrap the wire around the biggest drill bit I can place into the wick hole. I do that with the drill bit in the wick hole and hook up the wire before taking the drill out. I then make the SS mesh wick to fit the wire so that it goes in easily, but is a slightly snug fit.
This setup allows me to take the wick out and easily dry burn the
coils. I clean the wick in running water, pat it as dry as I can and put it back into the coil. This works very well for me.
If you are using a wire rope wick with SS mesh around it, I have no experience with this but I would try to handle it the same way.
If I could not take out the wick and wanted to clean the system I would empty the
tank and attempt to dry burn the coil and wick in place. Be careful not to overheat your hardware if you try this. I would flush the coil and wick with water afterwards and dry the wick as best I could. I have done this a few times with SS mesh, but it is more difficult to do than taking out the mesh.