How to get glue out of Dog's fur?

My puppy was playing outside in my neighbors back yard and he got stuck in a "rat glue trap"... We've been trying to get the glue out of his hair but it won't come out and sticks to anyone who touches him. We've tried Dawn dishsoap and still nothing... I'll proceed to trying peanut butter and see if that works.. Also, cutting isn't an option because he's a chihuahua dog and doesn't have enough hair to cut. The glue is on most of his face, completely coated on his two front paws and most of his stomach and back. Please help, for the sake of "Ollie".