Can I invite one cousin etc. without inviting the others?
The rule of thumb when creating a guest list , is to treat all family groups equally. Many experts so you must invite all of the cousins, etc. if you invite one. They will tell you that it will cause bad blood and arguments. I do agree that it can cause tension and possibly some unpleasant disagreements. But at the end of the day it is your wedding.
If you have people that you believe will be disruptive or misbehave let them stay home. This is a day that you will pay a lot of money and spend a lot of time planning. It is your wedding ceremony and reception. It's your special day. So you do what makes you happy.
Now, having said that I would certainly be diplomatic. You can always cover your tracks and just say that you are on a fixed budget and have a strict number of guest that you can afford to invite. You would certainly love to have them be a part of your day but your hands are tied due to the financial responsibility. That way you are not hurting someone's feeling.