I naively thought a 3 pin plug was a 3 pin plug and would be wired the same as a standard 3 pin 240v plug! Obviously not the case? I wasn't suggesting cutting off the lighter connection, just connecting it via a 3 pin to lighter adapter connector but the only 3 pin ones I have seen are 2amp not 10. There are 2 pin to lighter rated at 10amps but these seem to be 2 square pins?
The 3 pin socket holes on the boat look quite small pins. I am of course making the assumption that these are 12v sockets. There are 240v ones but they of course are 3 pin square ones.
You are comparing chalk with cheese but with possibly a lethal outcome - DC requires only two connections positive and negative, 240v AC mains three, live, neutral and protective earth.
If at all possible use dedicated low voltage DC sockets for your 12 volt distribution. For external use suggest these waterproof non-reversible plug/sockets.
For internal the Hella/DIN range are far superior to the awful although sadly common cigar lighter sockets which are hardly fit for purpose. See Alan 's post above!
The sockets are available as panel or flush side mount. Typical rating 10 amps. Both are available at most chandlers or from mail order marine suppliers.
The three round pin connectors I think you were referring to were designed to supply household mains table lights etc. Their rating was 240v 2 amp I believe. Whilst they do the job for DC distribution there is an unused pin and no convention as to which is positive or negative - best stay away IMHO.