Finding UK Companies with Product Directors and No Designers on LinkedIn

Hey all - long time Clay user/fan… I have another question. I think this is impossible… but if anyone is able to help, I’d be eternally grateful. Here goes: Our ICP is the following: Head of Product at any company in the UK that does not have designers. i.e. is there a way of finding companies that have a Product Director, but don’t have any designers listed on LinkedIn. Any help gratefully received.