I have used a Dremel, too.  And while I have not had the experience of Eric chewing blocks of wood into ducks, I have taken the tool to hawk, falcon, and owl beaks to trim and reshape them when they are overgrown!  
I am much more comfortable doing that work on a gunstock with hand tools now and will leave the rotary tool alone.  However, with the birds, I want it done and done quick to reduce stress and limit the amount of trust I am destroying by manhandling them, so Dremel it is!
Take your time, Cryo!  Don't let us pressure you into hurrying.  Enjoy the process.