To the best of my understanding, Father Brown's quote (in its entirety) would ask that one first deal with my oneself. He would not have you deal with just yourself rather than others. He would have you deal with yourself before you deal with others so that you may understand the darkness within ourselves and also to be compassionate when dealing with others.
In this sense to keep oneself safe and sane is to keep ones decisions and darkness in check.
As was pointed out on that other question you linked, this is a surprisingly tricky sentence!
Let's slowly build it up.
It will take someone else.
What is "it"? Stopping Voldemort again. Implied but never directly said. As for "take", we could say "need" instead, just to be slightly clearer.
[Stopping Voldemort again] will [need] someone else.
This isn't "someone else" as in "we need a different person", but as in "we need other people prepared to do what you did, Harry". When will they be needed? "Next time" (that is, the next time that Voldemort tries to return).
[Stopping Voldemort again] will [need] someone else who is prepared to [do the same as Harry] next time.
Now, Dumbledore is saying that this someone else doesn't have to do much. Hence, it will "merely" (or "only") take someone else. This may sound like it's demeaning Harry's efforts, but it's meant to be reassuring Harry: standing up to Voldemort is not very difficult or unlikely after all, and it doesn't take someone extra-special to do it.
[Stopping Voldemort again] will merely [need] someone else who is prepared to [do the same as Harry] next time.
What, exactly, did Harry do that Dumbledore says they need other people to do (or be prepared to do)? "Fight a losing battle"--or what seems like a losing battle. (Dumbledore omits the word "like", but I'll leave it in for this one example.)
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight a losing battle next time.
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight what seems [like] a losing battle next time.
And now we just replace the bracketed bits with the different wording Dumbledore uses, and we have the sentence (okay, part of a sentence) that you bolded.
It will merely take someone else who is prepared to fight what seems a losing battle next time.
Best Answer
Peppermints are, shall we say, not a normal part of a meal. Like all mints, they have peculiar effects on the mouth, changing the taste of anything eaten after them, usually not for the better. And peppermint in particular tends to be associated pretty strongly with toothpaste.
You will sometimes encounter after-dinner mints, which are often mint-flavored (not peppermint-flavored) chocolates, but could be peppermint candies (the round ones with red stripes), or even, indeed, peppermint humbugs. However, as the name "after-dinner mint" implies, these are something eaten after the meal, as a sort of palate-cleanser or breath freshener.
That all said, the passage doesn't imply any particular reason for Harry leaving out the peppermints, and there isn't a cultural reference that you're missing or anything like that. Harry could have been putting off the peppermints for eating after dinner, or perhaps he was just a sensible boy who didn't like his food to taste like toothpaste. (Disclaimer: I hate all things mint in any use other than toothpaste. Mint chocolate chip ice cream, in particular, is a mortal sin in my book.)
Note that "humbug" as a type of candy is definitely a British term: on this side of the pond, we only use the word "humbug" in the "bah, humbug" sense.