One of my cats has feline herpes. She gets L-lysine mixed into her food every day, and she has outbreaks where she's sneezy and snuffly for a few days. She has had a few respiratory infections during her life & we resolved those with antibiotics.
I don't close my cats out of the room while exercising. The herpes kitty likes that room, partly b/c there's a humidifier in there in the winter, I think
When I had two little kittens (herpes kitty included), they climbed on me during yoga. Cute but annoying. The other baby would try to grab my ponytail during crunches - painful but cute. They got over it, and now they mostly just watch; herpes kitty likes to lie on my belly during savasana sometimes.
I've never taken up kettlebells, partly because of the cats ... *flinging* weights around seems dangerous, lol. But mostly it's because I don't want to buy & store more stuff.