1) Identify the conditions which reinforce more swearing and stop doing those things. If saying "don't swear" makes him more likely to swear, don't say "don't swear." This sounds obvious in retrospect, but is very difficult to implement in practice because it's frustrating to not have any idea what you should do instead.

2) Identify the conditions which reinforce less swearing and start doing those things more. It doesn't sound like you've identified those conditions yet. This is the most important step.

To what extent does ignoring the problem work? There are probably certain areas where you should be ignoring it, and certain areas where you need to get more creative. The problem with using a strong punishment as your method as you've identified is that it can only be implemented after he gets home from school. Rewards for good behavior are generally preferable under such a condition as rewards are generally better than punishment at maintaining behavior. The way his teachers handle punishing the situation is probably going to matter a lot more than anything you do.