The comment of having a bottle to just "pour it on" is rather telling. We have this idea wounds should be dressed in ointments and then bandaged. A small amount of controlled bleeding will naturally flush any debri. Betadine and a loosly fitted bandage ( air circulation) are a good followup. I've seen to many horses ( and people) with injuries smothered in ointments not unlike cement repairs. The doctors/staff usually have to remove this stuff to see the extent of the wound, causing further pain and tissue injury.
Considering Betadine has the approximate viscosity of water, I don't see why this should be a huge issue. You can pour the stuff on or over the wound, dab or let the excess run off and you are set. It seems the really cool part here is that it is not a paste.
-john