First let me say that shakes are great: convenient and quick to make and full of goodness.
You need 5-10 portions of vegetables a day, the fresher and less processed the better so it would be hard to get them all in one sitting.
That said, get yourself a magic bullet blender. They are cheap, hard wearing and you can make loads of different shakes to whatever taste you like.
I will pick up on one thing you said though. You hate MOST vegetables?
That's like saying I don't like food. the term covers such a variety of foodstuffs you couldn't possibly hate most. I'll bet you have not even tried most.
Look at this list and tell me you hate over 50% of those veggies:
List of culinary vegetables - Wikipedia, the free encyclopedia
That's before we get into the thousands of different ways to actually cook them.
If you think you hate vegetables you are doing it wrong