I use tissue (Kleenex without the lotion), tortillions, stumps, even Q-Tips on occasion.
Maybe when the instructor said not to smudge, he/she meant don't do that with your finger, because of the oil that is in your finger.
This warning is also true for kneaded rubber erasers...don't ball it up in the palm of your hand while you work, or it'll get oily from your hand as well and this will transfer onto the paper.
If you want to get very nice even blending, you can't do this in a humid environment. I live in GA, so I sometimes have to turn on the air conditioner even on mild days, to get rid of some of the humidity so I can blend my pencil.
My artwork is primarily 2-B pencil, and sometimes I will use some black Micron ink for the darkest parts, but this is rare.
Sometimes I will do an intentional 'smudge' for backgrounds.
Embrace the smudge
