My wife has had a hysterectomy, so there is no chance of pregnancy. She refuses to have sexual intercourse with me because she doesn't like it. As a devout catholic, myself is it permissible for me to relieve myself under these circumstances or am I supposed to spend the rest of my life without an orgasm? I am having a really hard time with this.
In Catholic moral theology one is never permitted to sin in order to bring about a good. The reason for this is that when one compromises with evil even if it is to bring about a good evil has already won. When one adopts the ways of the enemy one becomes the enemy.
The answer to your question therefore is no. Masturbation is a sin and there are no circumstances that make it not a sin. I am not saying I don't sympathize with you. I am not saying your feelings are unnatural and I am not suggesting your desire is not an understandable desire. If you have engaged in masturbation I am not suggesting your are evil or bad because you have done so. It is a very common issue that all people struggle with at one time or another. Notwithstanding that we do not serve our passions, our passions serve us. Engaging in masturbation as a way of controlling sexual passions or relieving them essentially puts us at the service of our passions rather than the other way around.
When one engages in masturbation as a way of controlling one's sexual passions one actually risks making the problem worse. In other words our sexual passions will get more and more intense the more we engage in masturbation. Far from controlling sexual urges masturbation can make them worse. Eventually we can develop an addiction to masturbation. The more intense the sexual passions, the more intense experiences one will begin to seek out--which can lead to adulterous actions--such as pornography or worse: hooking up with escorts or exotic dancers.
Some may disagree with this assessment but it makes sense to me. You have to keep in mind we are also living in a society that resents any notion that we should seek to control our passions and urges. Today--the only restraint society seems comfortable with is in making sure whatever you are doing is between consenting adults. I note however that even that restraint is going to come under attack as our society continues to distort the purpose and meaning of human sexuality.
This can also lead to a lack of interest in your wife. I read somewhere that men who look at internet pornography eventually become board with their girl-friends or wives and would rather the pornography! While some might disagree with that finding, I can say that this makes sense since the world of pornography is a fantasy land devoid of reality.
Notwithstanding the above every man who has ever lived has engaged in masturbation whether they were single, married or just dating. I remember reading a statistic that went something like this: "98% of men admit to masturbating, the other 2% lied." It is something that all men struggle with, and is normal even though it is technically sinful. Again, it is seen as a sin because in order to orgasm one must imagine sexually stimulating images. This means women become objectified--that is they are not seen as a human being with real worth but an object solely for one's sexual pleasure. That is what makes masturbation sinful. Masturbation turns sexuality on it's head because it makes the meaning and purpose of sexuality solely about pleasure not love.
My bigger concern here is not masturbation but the fact that your wife does not want to engage in the martial act. This suggests there is an issue that needs to be explored. You say she refuses because "She doesn't like it." What does that mean exactly? Don't tell me---because this is not something that is appropriate to discuss on a website. My point in bringing that up is that her statement needs to be explored and discussed to find out what the real issue is in her mind. Since I am not a professional counselor or marital psychologist I can't even begin to guess what that issue is. It is something I would recommend that both of you explore with a professional counselor.
You ask whether you can "relive yourself" since your wife does not want to have intercourse. Relieving yourself might make you feel better in the short run--but it won't solve the larger issue, namely that your wife does not want to have intercourse with her husband. That is the real issue here and that is the issue I suggest you and your wife explore together--if necessary with a professional.