Mine seems ok with vaporub (on me) too. But I did read the warning about essential oil diffusers this morning - so I thought I would mention it. Bad enough to get the flu, but terrible to have a dead kitty at the same time.
What might work would be to mix the oils with a neutral carrier like olive oil or petroleum jelly or lanolin and rub it on your chest or on your shirt a la Vicks. Then it’s where you can breathe it without filling the room with something that will be noxious to your pets.
Cats being curious, they’ll probably nose up to you anyhow.