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.

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 👀

I always answered no

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

I think they will