From the way you've told it, you should be OK but it might be worth getting some legal advice in your own country as to whether you actually have a criminal record or not. In the UK, minor convictions like this become spent after a period of time anyway. Reading again, it sounds like the UK equivalent of a caution and they don't appear on criminal records searches.
It was nearly ten years ago and even if it still stands, I'm sure most people would be sympathetic given the nature of the misdemeanour. However, if you need to recount the circumstance, be wary of including emotive phrases like "cops had to something to prove"; it wouldn't help your case!!
Cheers
Whirls