I'd suggest this isn't your monkey Joshua.
On the surface the problem is very simple: does the item you made that was exploited by the company need a CE mark or not? If it does, then you produce the Technical File etc. as you described.
Unfortunately, your H&S department may have lifted the lid on a much more serious issue. As a business it appears that your employer does not understand the rules behind CE marking. (Or at least they've not been able to explain them to you!) The implication is that the business may not be meeting it's legal responsibilities on a larger scale, and that they will be liable if something goes wrong.
I think this is one for your manager. Ask him 'What's the company Policy on CE Marking' If there isn't one, suggest politely that's a management problem.
You may be unlucky and be given the job of writing the Policy. Not impossible, you wrap a wet towel round your head, take advice, and work out the answer. Even better, pay a consultant to write it.
Once the policy has been signed off by the boss, whenever H&S ask about CE Marks, you tell them that you follow Company Policy. And a Policy is a jolly good thing to have in the event the Company gets sued: it proves the business is not negligent and/or incompetent.
Putting this tactfully could be a good test of your people skills!
Dave