Here's what my DA dogs do: if a male dog comes close and starts the usual canine greeting rituals of sniffing and such, they tense. If the dog persists, my two get aggresive. It's not even every male dog...I'd say maybe 7 out of 10 gets that reaction. And they ONLY do it when not under my direct control. If I am there to intervene and tell them "no", they will not react. Or, at worse, will only be with a growl and a snap.
The reality is that you probably wouldn't ever have a park to yourself. That doesn't happen in a public place. People use dog parks at all hours of the day and night, particularly if dog parks are limited in the area. I've been out as early as 5am in the summer and seen others at parks.