Its a shame that the stems below the internodes are so short. An Internode is capable of producing a root, or a new shoot. You want to plant the whole node (with the emergent root) in the soil. You can use a very sharp knife and try to cut back as little as possible. Just until you see green and the black/brown is gone. I would clean my tool with Isopropyl (rubbing ) alcohol first and allow it to dry before making any foray to remove any stem. Then dip in the fungicide powder. If you cannot locate Captan, you can also use a rooting hormone that CONTAINS fungicide.
Captan is the only fungicide I use personally. I do not spray anything like copper fungicide or Funginex (the liquid fungicide used for roses and such). I like to be able to control exactly where the fungicide goes because they are undesirable to broadcast widely. If you use something else, it will probably be ok, just dip do not soak in liquid fungicide.