Another approach is to divide unpleasant work evenly under everyone who can do it like in the novel The Dispossessed. This will be less efficient since each one needs to acquire the skill and won't reach perfection because they don't stay long enough but to hell with efficiency.
So yes, it is skilled labor and if you call it "unskilled", you have no excuse not to do it from time to time.
There's also the fact manual labor is seem by Anarresti as something to be proud of.
Also, Chevek doesn't directly mention it in the book, but in reality some people simply enjoy hard jobs and would gladily do them if they can make a good living out of them.