I use paper stumps and baby oil, too, when I'm not using my Copics. They are a lot of fun and give a well blended soft look to the images.
Paper stumps are shaped like pencils (only you get them in a variety of dimensions) andt they are made completely of paper. When they get used and need "sharpened", you use a piece of fine sandpaper to do that.
Here's a link that shows pictures of them...
paper stump - Google Search