If when filling out a job application form, it says have you ever been dismissed from a job, what would you do, if you had been dismissed but took an out of court settlement over it rather than going the whole hog and going to tribunral and the exemployer is no longer in business?

well the fact they settled out of court suggests you might have had a case against them, which is good if you do inform the new employer.

on the other hand, if there is absolutely positively definitely no way the new one would ever find out…

hinesty is always the best policy but if the odds of being found out are low – could someone there know the company or the history or a customer?- then only you can decide the risk/benefit.
It would be instant dismissal if found out. How about something like
I have an exemplary employment record backed up with references from previous employers. I was once unfairly dismissed from one employer – state time ago if ages ago-and the case was settled in my favour in an out of court settlement. I hope this unforunate event will not discourage you from employing me. I am happy to disuss this issue with you at interview if selected.
Dont bad mouth them at an interview if asked say it as unemotional weighted as you can.

Unless it involves security clearence, they can't check up on sod rock all. Most companies doen't even bother to collect referances anymore, as long as you give contacts where they can be collected.