I have a Cavalier King Charles whom we all love dearly, I also have two cta who he loves to bits. They are his best friends and he there's. This breed gets along with everyone and anyone...
To be honest worry more about the cats, I too have just bought a CAV and have two adult cats and the CAV just wants to play and chace them but the cats are a little scared and dont want to play with her.
I just got my 5 1/2 month old Cav 6 days ago. My 8 year old cat is already very interested and the two of them were on my lap together last night! Just be sure to control the Cav so he doesn't scare the cat. The introduction should be gentle. I had to put my 16 year old dog down 6 months ago and know the cat has missed her. She now has a new friend!
I have a cavalier and she chases my cat just as she would chase a squirrel so it can be difficult at times. What we have done is designate a room as the "cat room." You can either train your dog not to go in a certain room or put up a baby gate so the cat can have some quiet time.