I would not muzzle a puppy. The pup and the cat need to be taught how to interact. muzzling isn't going to teach either one of them anything, except maybe frustration and confusion. They need to learn how to live together. My best advice is to stop this NOW, no more chasing, AT ALL.
The puppy can be kept on leash in the house, and when the cat approaches, TEACH the dog LEAVE IT. use the leash to empower your words, and use high value treats to reward the pup when he listens. The best idea to teach the dog to LEAVE THE CAT ALONE, and never ever allow the pup to chase the cat. playing can quickly get carried away, and have tragic consequences.
To keep the cat away from the dog, use a squirt bottle. if the cat approaches the pup to instigate things, the cat gets squirted!
until both have learned how to interact, do not leave them alone - and always supervise ANY interaction. even silly play can result in serious harm for one of them - a claw in the eye, a bite, etc….
Until I was certain my dog would leave both of my cats alone, I kept him crated when left alone, to be SURE no one got injured.