Anything that a puppy can ingest, that isn't meant to be ingested, could cause breathing/choking issues. It would depend on the amount of "fluff" consumed from said tennis ball as to whether or not that is the issue.
I would not rely on what an assistant told you over the telephone and would strongly urge you to take your puppy to the Vet as soon as possible if this hacking continues. It could be indicative of so many other things and should be addressed as soon as possible. Furthermore, if it is from ingesting something, the Vet will need to make sure that a blockage isn't likely to occur.
Please be very careful with all toys that you give to your puppy. If any bit of that toy can be removed, it goes in the garbage. My older Cavalier, (very small breed) has the jaws of a shark, and did have as a puppy. He actually destroyed the black Kong which is sold claiming to be "indestructible" and intended for large breeds with strong jaws. It took him 15 minutes to break a tiny bit of it off, and he ingested it and was extremely ill! That was nearly 9 years ago, but it just goes to show how we can't trust what the manufacturers say about the durability of their toys.
Good luck to you, and do let us know how your puppy is doing.