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.