What about one of the toe-up cast ons? Like Judy's Magic Cast On
or Turkish Cast On
? Except you'd start with casting on 20 instead of 10, since I'm guessing the muzzle is basically the toe of a sock. So a Toe-Up Cast On would work right?
ETA: Well with Judy's MCO you'd cast on 20, Turkish you start with 10, knit into them and end up with 20.