Cigarette lighter plugs/sockets are not the ideal 12v connection, especially for higher currents and semi permanent
installation. They are rated up to 10A some even to 15A, but I would be reluctant to use them for anything more than half this amount. I have seen several that have melted.
The Engel fridges use a different
compressor design to most fridge units. One advantage is that the maximum
power draw is quite low. It is around 2.5A for the smaller units. At start up, fridge compressors can demand very high currents for a short time, but it should be low enough that the cigarette lighter plug socket is acceptable.
However, in a
marine environment it easy to get some
corrosion, so keep an eye on the connection. An easy way is to check if it is getting warm.
A good alternative is to cut the cord and install a more reliable connecter like an Anderson plug on both sides of the joint. Thus the same cord can normally be used with a more reliable Anderson plug to connect to the
boat, or a cigarette lighter adapter, similar to the one shown, can be quickly plugged in for use in a car.
Anderson plugs have silver plated contacts. They lock together and are rated up to 50A without being bulky.
This gives you some idea. This was an adapter I made so a cord with an Anderson plug on one end (not shown) could function to supply the
power to a large capacity emergancy
bilge pump, or with the shown adapter a wandering 12v cig lighter socket. In your case you would have a male cig lighter plug.