It sometimes helps to put a slight bend in the pipe cleaner, I do this by inserting the pipe cleaner in the stem about 3/4” or so and bending the pipe cleaner down a bit. You don’t need a large bend, just a small bend, this can allow you to ease the pipe cleaner through a bent stem easier, you might still need to turn it left or right, but this will usually avoid scraping. This can also help you to get into the bowl on pipes that aren’t drilled perfectly. *Also* Make sure you are buying decent pipe cleaners, as shitty pipe cleaners often have wire extending well past the fluff.
I use this method as well.