'A tinker's damn is a British expression of contempt for something considered insignificant. In common usage, the expression is used this way: "I don't give a tinker's damn what the Vicar thinks", or sometimes shortened to, "I don't give a tinker's about the Vicar." In this context, the speaker is expressing contempt for the local clergyman and his opinion. A tinker's curse was considered of little significance because tinkers were reputed to swear habitually.' (Wikipedia)
However, if we're comparing cusses of tinkers, tailors, soldiers and spies, I would have thought a soldiers cuss would be equally prolific, hence the term 'swearing like a trooper'.
The term 'tinker' being a slang term for an Irish traveller (unsure of the level of offensiveness as it's not a term I've heard for many years) and the current most famous traveller being Paddy 'Big Brother winner' Doherty - a man who rarely swore and referred to people as 'sausages' - leads me to believe that the proliferance of 'tinkers cusses' has been overestimated.