We use K9 Advantix and we have cats. As long as your cats don't touch it on your dog until it's dry then they'll be just fine. It's only toxic while it's wet. We've used it for years and have had no problems at all.
And our pup has tested negative for Lymes every time.
Ask your vet, they'll give you the best advice for your situation. If he's outside most of the day put it on in the morning and by the time he comes in for the day it'll be dry and you'll have nothing to worry about.
Some days are curlier than others.