In order for your major to punish the American for a "criminal act", the major must have some kind of real authority over the American. Then, the punishment must be a legal one. It all starts getting a bit convoluted and difficult to figure out - which is often a signal to pull back and rethink. One of the most irritating things for a reader is when a character only does something because the author needs him to do it for the plot. It works much better if the action is something the character would do anyway.
It sounds like your major isn't acting in an official capacity - going around kidnapping people and so forth. So in order to express his frustration and displeasure with your American, you may be best off just having your major take the time-honoured route of getting a couple of his henchmen (he's British, and everyone knows all British people are evil - just ask Hollywood; we have henching lessons in primary school when other countries are teaching things like arts and crafts) and taking the American behind the tents and beating the sh*t out of him.
Beating the sh*t out of someone has the advantage of being a) universal, b) unofficial, c) traditional, d) not requiring any specialist equipment or skills, and e) infinitely variable for narrative purposes.
Plus, how you arrange the participants can tell you a lot about them. Is your heroic American being held down by evil henchBrits? Who is doing the actual hitting? The major or more henchmen? Does the major take any part in proceedings, except to supervise - superciliously? Or does he get his hands dirty? Does he take any risks, or has he made sure that the heroic American is being restrained by the henchmen? How do the henchmen react? Are they silent, stone-faced minions, or are they enthusiastic?
Your American can be properly heroic by trying to fight off the cowardly Brits, but still be left for dead by the laughing major and his henchmen. Naturally, there will be enough henchmen to ensure that your American is going to get thoroughly beaten up no matter how bravely and well he fights back. And, of course, your American can be even more brave etc, by dragging himself off and sewing up his own wounds without anaesthetic.
I wouldn't go with bullwhipping, for the following reasons:
- You need a bullwhip. Why would your major have one to hand?
- Bullwhips are specialist equipment. Not only do you have to know how to crack them but they're a distance weapon, and you have to know how to aim properly. Bullwhipping someone takes practice: believe me, I've tried.
- Bullwhips aren't really a British thing. They're more American, so why would your British major have one - or know how to use it if he had it? You would have to set this up in the story beforehand (and even if he is a bullwhip aficionado, why has he brought one on campaign with him?).
- Because it's a distance weapon, you need to make sure your victim doesn't run away. So that means you have to tie him up, then stand back and bullwhip him. Probably you need henchmen for this, because wrestling with your victim on your own is not necessarily a great option: he might win (especially if he's a heroic American).
- And because of that, unless you're really into bullwhipping people, it's just not as emotionally satisfying as punching someone in the face. There's something about that physical contact between fist and physiognomy that really, really, hits the spot (!) when you are expressing your deep disapproval of someone's life choices in the immediate past, and how they have negatively intersected with your plans for the future.
- It's also complicated. If you need to get the henchmen involved anyway, just take the American behind the tents and beat the sh*t out of him. It's quick (or slow, depending on taste), it does the job, and you can either watch or participate according to taste.
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