Take the ferry!
The short ferry trip likely results in lower emissions of CO2 compared to the long detour, if the EV is charged from a grid that uses fossil fuels (coal/gas).
I think there are actually three different change scenarios worth considering here.
- Marginal: You change your route, but nobody else does. (This is looking at the problem from an individual "carbon footprint" perspective).
- Group: a significant number of people all change their route.
- System: the ferry is shut down entirely.
Marginal Scenario (one more car on the ferry)
From my reading I've learned there are several factors that significantly impact fuel usage and emissions on passenger/vehicle ferry transports (eg. trip frequency, speed, prevailing winds, vessel size, fuel type) but number of vehicles on board is not a significant factor. (disclosure: I am not a marine engineer.)
Although I think your assumption about ship's fuel use (below) is intuitively correct, it's such a small factor that it doesn't make a significant difference and cannot be reasonably measured.
However this ferry will carry +2 tons of cargo (car+me) which will consume more fuel.
Although it's tempting to use a measure of fuel use like litres/passenger-km to estimate the impact of a single trip, the reality is that the actual carbon emissions and air pollution don't really change in any significant measurable way whether you board the ship or not.
Therefore, you can assume approximately zero emissions for the diesel ferry. On the other hand, natural gas peaking plants are designed to scale power output up or down based on power demand from the grid, so using electricity to charge your EV likely does result in a very slight marginal increase to carbon emissions and air pollution.
Winner: Diesel Ferry
Group Scenario (many more cars on the ferry)
Vessel speed and number of return trips have a very significant impact on fuel usage. If many more people decide to take the ferry, the ferry may need to perform more round trips and/or operate at a higher sailing speed. (Although sailing speed probably doesn't matter much for a very short-haul trip like the river crossing you're asking about.)
If the ferry needs to make an additional round trip to handle increased demand, then we can distribute the fuel usage across the group using a measure like litres/passenger-km. Luckily there's a study we can refer to: Comparison of Ferry Boat and Highway Bridge Energy Use.
Examinations of three of the systems found that the passenger-MPG of the ferries ranged from 2.61 to 14.00 (1.11 to 5.95 km/L) [0.90 L/km to 0.16 L/km]
On a per-passenger basis, your 0.16 km river crossing would use between 0.0256 - 0.14 litres of diesel fuel. Diesel engines produce 2.7 kg of CO2 per litre of diesel fuel consumed.1 So a single trip by diesel ferry would result in around 0.07 - 0.38 kg of CO2 emissions.
Electric passenger vehicles typically use around 20 kWh/100 km, so your 15 km drive would use around 3 kWh. Natural gas peaking plants emit 0.91 pounds2 (0.41 kg) of CO2 per kWh produced, so the 15 km drive would result in 1.23 kg CO2 emissions.
Winner: Diesel Ferry
[Maybe I'll add this in the future. This answer is already quite long and I have to stop for now.]