Wow, false binary much? I guess if we were magically transported to a universe where those were the only two options, I would pick the list? Over cheating on your wife? It's not entirely clear to me what the denied list would accomplish. Does she just not believe that you aren't having sex?
I mean, I get the sense that what you want me to say is "Gosh, if you've even resorted to washing yourself and your wife still won't fuck you, I don't see any choice for you but to pay someone else for sex. It is practically required!"
But it seems to me that the first step in all of this is to say, "Hey there wife of mine, I've noticed that you aren't interested in sex with me lately. What's up? Are you ok? Is it something I am doing? Because I would like to have more sex." What you learn might surprise you. I suspect your wife has her own whole set of reasons for wanting or not wanting to have sex. Reasons you could then talk about as a couple, and try to find a resolution for.
Who knows? You might even realize that your sex drives are really different right now, and decide together that you getting a little something on the side is a good solution. Which, great! I just find it sort of troubling that you write about your wife like she is some kind of wall safe that contains a pussy, and if you can just find the right combination of actions, you can unlock the safe and fuck that pussy.
That is not how wives are. They are human beings with complex thoughts and needs and emotions and desires, all of which might affect when and how they want to fuck their husbands. I mean, you know this. At least I hope you do.
And if things aren't working out between you guys, then that's something else too. I personally am on the side of honesty and communication and finding extramarital solutions to sex problems if you feel your relationship is good but the sex isn't, but I do understand that some people honestly feel that cheating is the right and least hurtful thing to do for both parties. I'm not in those people's situations so I can't say. I just know I wouldn't like it.
Also? Marriage is fucking hard sometimes. Maybe you'll talk and find that she's depressed, or going through some shit, or any of a million reasons why sex doesn't sound very appealing right now. Sometimes being married might mean not getting laid as much as you want. Like anything, you can either choose to change the situation or your mindset.
But at least find out what's going on with her, you know? And not just for your dick's sake. And in the meantime, in terms of the bursting issue, masturbation is free, bro. Look into it.