With the Large Hadron Collider being a powerful particle accelerator, is there any evidence of the scientists working on it suffering from any cancers?
The machinery is dangerous, but not in the way you're thinking. Accelerators come with a lot of extra equipment, like high voltage power supplies, vacuum pumps, cryogenics, sometimes pressurized gases, heavy objects, confined spaces which could quickly become oxygen-deficient if there's some sort of gas leak and too much air is displaced. Then there's the hazards of working around high magnetic field strengths (bad if you have a pacemaker, could also wipe your credit cards).
Then of course, there's the possible exposure to radiation. But at any accelerator facility there will be strict interlocks and procedures in place to make sure that nobody is in a room where beam is being delivered. There are radiation monitors everywhere, and any number of different control systems which can very quickly shut off the RF for the accelerators if necessary.
"Radiation workers" have certain yearly dose equivalent limits that we're allowed to sustain. At least in America, it's below the threshold for noticeable negative health effects. Whenever we're in a part of the building where there could be radiation, we wear dosimeters. Dosimeters record the dose your body receives, and typically get sent in every few months for testing. It's rare for any issues to arise. We follow ALARA (exposure should be As Low As Reasonably Achievable) whenever handling radioactive sources.
So if you do something very stupid, you could get hurt. But the same could be said about just about any profession. Just going outside and driving your car puts you at some small risk, but most of us do it all the time without worrying much.