The tunnels are in Baltimore. You have no choice but bypass it if you plan to take 95 to get from New Jersey to North Carolina. Whether you stop in DC or not doesn't make a difference.
The detour around the tunnels is simple and traffic is actually less. Take 695 towards Key Bridge back around to 95. There will be a toll. If you must avoid tolls altogether, take 695 west the other way around Baltimore. This will be longer and the road a little more congested, but you will avoid tolls.
To be honest, I wouldn't stop at Cherry Hill Park unless I planned to stay for a few days. You see nothing of DC there and it might as well be in New Jersey.
I would also try to time my trip so that you arrived at 695 after 10AM but before noon. This would put you in the area of Cherry Hill Park between 11AM and 1PM. If you arrive in the Cherry Hill Park area before 12PM, you might consider continuing past DC and stopping further south, around Fredericksburg. This will get you past the worst of the DC/VA traffic by 2PM, when it starts to get really bad.
2015 Jeep Willys Wrangler
2014 Fleetwood Bounder 33C
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more than 1700 days on the road