I'm thinking of walking my dog in a "no dogs allowed" area
It clearly says not to. Is there a particular reason why you want to?
I walk my dog there all the time and the police don't pay attention to it.
You want to walk your dog anywhere you please, but this can still look bad on you. Even if the rules won't be followed up by the police, it is good to get used to them. Next time they do enforce them it wouldn't be much of a shock to your system.
Having a segregated dog park or designated area will not do much to make the dog have an enjoyable time. My dog enjoys this restricted area.
I'm glad your dog finds that place nice, but there are rules and reasons why he shouldn't be there. What if that could be somewhere dangerous, and you are risking your dog's life there? I think you should just try to find a new place he would love, just to be safe.