M.L.
This is part of your toddler's task of trying to figure out the world he lives in. Yes, why not ask him what the trouble is with cat hair? He's not afraid of his cats, right?
But he may have trouble verbalizing what the bad feeling is. Is he worried that the cat hair means his cats are sick, or going to die? Does it mean that there's a scary cat waiting to pounce on him from inside the sofa cushion? Does it mean that the whole house is turning into a giant kitty?
I would ask him, and if he can't answer I would bring up a suggestion like that - very casually, as if you were just curious. Maybe you'll find the answer that way. Then you can say, "Have I got a great surprise for you! Your kitties are fine! They leave their hair on the sofa because they have too much and don't need these bits - and they want Mama to have the fun of cleaning it up!"
Or, "Have I got a great surprise for you! That hair is not going to turn into a monster kitty! It really belongs to Muffy and Peaches, and they don't want it any more. So we'll clean it up right now and take it outside to the garbage can, and then you can tell your cats that the job is done." You'll be able to think of something that fits the case.
The thing you don't want to do is to laugh (even though it may be funny). Let your curiosity and your casualness help him get over his fears, but you also want him to be able to come to you with anything else that may bother him. I've read that children don't have imagination and reality truly sorted out until they're six or seven.
P.S. Just read your P.S. Yes, illness can do a job on a child. Patience and lots of TLC, too!