I suspect people are making this more complex than it needs to be. For most of these tests the difference between a good score and a poor one are just a few questions.
So, the first step is just to actually take the test. The cheating bit would be having someone monitoring what your doing via a reasonably hi-res hidden camera/etc pointed at your screen/etc. Then all you need is a channel for that person to communicate with you. Be that a tiny bluetooth hearing aid in one ear, a phone/screen taped hidden on your leg/etc or to your existing screen. Basically somewhere not visible to any camera's monitoring you.
So, when the person monitoring you detects you have answered something incorrectly they send you something to the effect "question #5's correct answer is Y because A,B,C". Then later you get a moment of insight and go back and fix the problem. In theory, unless your completely clueless the difference between a 2 and a 4 is just a couple questions so this would only have to happen a couple times during the whole test. Again, unless your completely clueless, if the proctor notices you fixing an incorrect answer and asks "why did you just change your answer" you give them something reasonable sounding. Heck for some of them, it might not even have to be the right answer, its completely possible for someone to get the right answer the wrong way in a multiple choice section. AKA, "I guessed on that one the first time and A & B seemed far fetched so I just picked C over D, but then later I questioned my assumption and decided it was B & C that seemed far fetched so I picked the remaining answer which was D rather than A".
Anyway, I'm not sure the screen is needed. For a test that is 100% multiple choice, a buzzer in your shoe would be enough if it went off whenever you selected a wrong answer, and then pulsed a code to indicate the right answer.