Thanks for the clarification.
In addition to what MediumRare says, I think you're probably off on a number of things. Consider:
Beloved, never avenge yourselves, but leave it to the wrath of God, for it is written, “Vengeance is mine, I will repay, says the Lord.
You have heard that it was said, ‘An eye for an eye and a tooth for a tooth.’ But I say to you, Do not resist the one who is evil. But if anyone slaps you on the right cheek, turn to him the other also.
You get the idea....
Also, I think you're probably way, way off on this:
If you piss on me on purpose I'm going shit all over you in the worst way I can.
Your W may have been mad enough or resentful enough to want to hurt you, but in all likelihood, om didn't think twice about you.
In most cases, I'm convinced that BSes are really just collateral damage. Sorry.
ETA: One of my guesses is that you think the A is an attack on your sense of being a man, and/or you think others will think less of you because your W cheated.
I think it's true that others who have not been affected by infidelity may think less of you (if they knew). In fact, however, your W's cheating says absolutely nothing about you or your abilities.
Except in very rare cases, being a cuckold doesn't show up in a way that others can see, so you don't have to give any energy to what others might think. I've met a number of BHes at g2gs, and they all seem like strong, capable men to me - and I know they're fBSes. And then there's the former state governor who took his W back after she lived publicly with om for more than year ... I think he could still be governor, except for his desire and/or term limits.
(Of course, if you out om on the 'net, you basically out your W, and that outs you, so you'll get a good test of how people will treat you knowing your W cheated.)
Another guess is that you may have some sense of owning your W - that's the only way I can see for you to think om did something to you when he and your W were doing each other.
In fact, your W is an autonomous adult, and you don't own her in any way. She has many obligations to you, but that's way, way different from owning her.
Your W's cheating reflects on her character, not yours.
What's your goal? You're stuck as a cuckold - there's nothing you can do about that. That's beyond your control. Nothing you do to your W or to om will take that away.
The only goal that makes sense is to heal, and that requires you to focus on feeling good about who you are and what you do. You've been 'thinking' this through with a brain clouded by anger, and you're doing yourself a major disservice. You've got a lot of grief, fear, and even joy inside, and you need to acknowledge and process all of that.
I don't know anything about Brazilian Jiu-Jitsu, but in the East Asian martial arts I've come across (Tai Chi Chuan, Aikido, Judo, Krate, etc.), acting out of anger is one of the primary types of action to avoid.
And yet that's what you're contemplating doing and defending. I don't know whether to say 'Bullshit!' or to plead with you to get grounded before you do this....