I would suggest buying some time like 2 or 3 years so that you can sort out some basic issues that will affect you in later years. Now, kindly put away any impulsive and emotional feelings aside as you ponder over these things. Do not decide in a hurry, but take time and decide only after you are fully convinced about things. Until then, commit to nothing.
This is your marriage, supposed to be a lifelong event. If you are easily pressured into the marriage by family elders, you are not really ready to be married. You need to know the consequences of yielding to this pressure. First of all your communication with your partner will be dictated from others much more than from you, simply because you just obeyed orders. Things will get worse when you have children. Again pressures from relatives will make you a rubber-stamp and you will have a very hard time trying to change things at that point. In all this you have not mentioned if the bride is also getting pressured into marrying you. If so, then your problems are multiplied and you can resign yourself to a life of misery and unhappiness.
Times have changed, and what was well accepted one generation ago is not acceptable today. Today's children will question you and look down on you when they find you married against your will. They will question you and even sue you 15 years from now about why you made this decision knowing well that there can be genetic problems/consequences of marrying close relatives. Do you want to face all these things and more?
Your chances of getting children with genetic disorders are high, since it seems from what you wrote, both bride's and groom's parents are wanting this. I am estimating that they have also been marrying close relatives for over two earlier generations, and possibly a lot more because of traditions. You can make a simple calculation from Mendel's experiments with green and yellow peas which you might have studied in high school. Chances are 1 of 4 in the initial levels and then it goes to 3 of 4 down the line. That means of 4 children you may have at least 1 will be affected and you won't know the order if the 1st child or 2nd child etc will be affected. This is simple check up. You can always go to specialists to get specific info a they would dig a lot deeper into various health issues in your family hierarchy.
Considering the above, your best options, I think, are to delay immediately. Then take time to see where you really stand, and how you want to lead your life. You have to have a change in mindset about traditions. Some traditions can be very wrong even if is accepted for generations of time. Your family elders will logically pass away before you/your wife and children do. So you will have to be ready to take decisions at that time, but it may not work out for good as you have not made decisions and choices earlier, yourself and in consultation with your partner. You might end up running after some other elders instead of being a man yourself. Your children will need role models and leadership/shepherding, and they definitely need NOT see their parents pushed around by other (well meaning) relatives. That would severely damage your communications with them.
So you do have some tough choices and you need to develop your own self respect and ability to lead your own family. You can certainly do them, and your starting point will be to delay any happenings and commitments. If you do the first step and not fail under the sure-to-come scolding and emotional (not rational) threats, that itself is a big progress and you will be well on your way to ensure life is joyful to a great extent.
Wish you all the best as you plan your future wisely.
Never spend what is not yours!