When I’m applying for a job and they ask if they may contact my last employer and I say no .. will they find that sketchy ??

If you're defensive probably. If you're honest and give a straight forward answer "we didn't part on good terms, I'd rather not discuss it" should be adequate and then never mention it again, my new boss asked why I quit my last job "I found it extremely unsatisfying " leaves out all the details and no one is getting bad mouthed.

I always answered no

I think they will

Just say that your last employer was the CIA and they cannot be contacted because you were in deep cover and have been given a new identity 👀

If they do contact the last company. They are not allowed to say anything negative about you