They also exist because there's important differences to the jobs. For example, in how you hire. If you're looking for "unskilled" workers, you can cast a wide net with the job ad and hit mostly the relevant audience. You can go up to anyone looking for a job and offer them said job. If you need a bigger pool of people to hire from, you can make changes that have almost immediate impact (e.g. increasing benefits, working conditions, marketing). For "skilled" labour, there's fewer people in the pool to hire from, so you want to go directly to where they're being trained (e.g. job fairs at universities or trade schools), and if you need to increase the pool you can hire from, that has delayed effects since you need to wait for people to go through their training.
I was not aware of the negative connotation though, so I'll keep that in mind. I don't think changing the word itself is going to do anything about that though. Connotation will follow unless you change people's attitudes towards these jobs. I don't know how you would do that though. Any ideas?