One thing you can do is to give the cap a squeeze between your thumb and index finger to push it slightly out of round and thus tightening the fit.
Of course, nipple replacement is the better solution but squeezing is a doable method when you need one immediately.
You have elevated barking to limbing. Much more difficult given the small diameter of the twig!
This begs that you elevate your game to "grinning" the squirrel as Davey Crockett did. And, you can surpass Crockett in that he had to "take a rest" for his chin. Your challenge will be to do it "offchin" without a rest. Once you master this you could leave your Crockett at home. But we all know you would never do that although you might admit to never loading it.