I believe you need reservations for the car. I assume that would be for a specific sailing time, but don't know. I have only done the ferry as a walker. We were there a couple weeks ago and noticed long car lines for the ferry, but I don't know if that is typical. Should be easy to check the requirements online.
Helsingor has a charming central city area. Probably you could park and have a walk around. I'm trying to remember how impressive or non-impressive Kronborg was from the parking lot. I think it is probably worth passing by, especially if you stop in town for a short stroll. If you happen to get there quite early, we were surprised by how much we enjoyed the Maritime Museum which is right next to the castle. We stopped in only because we had the Copenhagen Card so it was free for us. We ended up staying 90 minutes and wishing we had longer.
Not much help from direct personal experience, I'm afraid! I think if you find the ferry reservations easy (or that there is no need for reservations), it might be fun to do something different than the bridge. I don't know when you are traveling - perhaps the situation is different outside of summer travel time.