I think I get it. I understand what you are up against here. I’ve had similar situations. Not related to sex but hierarchy. But generally trying to use my expertise to make the end output safer, more effective and make the experience of the end user better and the people delivering the output thinking that because they are in a certain role they can dismiss what I’m saying.
With your role it sounds like you have very clearly defined actions that are required and a clearly defined way of reporting it which is helpful. Hopefully you also have audit processes for this and if you don’t, then start that.
So in your shoes I would let go of any emotion attached to a bad outcome. If something bad happens because he’s not followed procedure then that’s on him. You can’t make him. All you can do is your job to the best of your ability and flag up possible risks if you see them.
What you can do is dispassionately go through the motions each time, document it (cc’ing emails is a great way of doing this very transparently). Never mention what he has or hasn’t done - talk about what did or didn’t happen. So instead of ‘Joe arrogant-pants was required to do X but didn’t’ put ‘I am aware that XYZ has not been recorded. This concerns me in role as XYZ with responsibility for XYZ. This is because if it isnt done then then the risk is XYZ. If it was done but not recorded then the risk is XYZ. I am happy to rethink the recording system with (person responsible overall) if it no longer serves its purpose.’
So talk about systems, practices and actions without ascribing any responsibility or blame. Without talking about your own feelings. Just your roles and responsibilities. His line manager is responsible for managing him if he’s not doing what is necessary.
Your job is to flag up anything that compromises safety. If you do audits and present them dispassionately, over time it will be clear which team are not doing the do, and his ego will make him then be the best at it.
From the little bit you have said, I am leaning towards him possibly having a narcissistic personality style, at least to some extent. Look up Jefferson Fisher on insta. Really quick video’s of helpful communication advice.
Good luck.