I just dyed a bow yeaterday and glued some skins on. I used the same dye, but I used Titebond hide glue fer the skins. It works real well. I find the hide glue to be a little thick to work with, so I cut it with a little water and mix it up real well before I glue the skins on. No problem with the dye runnin on me.
TheWildCat