Well, there is the unbelievable story about a guy who actually put his head in a proton beam, the Russian scientist Anatoli Petrovich Bugorski. This happened at the U-70 synchrotron, near Moscow at the Institute for High Energy Physics.
But the thing is, is that he actually didn't feel any pain. He did suffer from epyleptic attacks and damage to his skin and brain. Citing from:
Bugorski was leaning over the piece of equipment when he stuck his head in the part through which the proton beam was running. Reportedly, he saw a flash “brighter than a thousand suns”, but did not feel any pain. The beam measured about 2000 gray when it entered Bugorski’s skull, and about 3000 gray when it exited after colliding with the inside of his head.
To be clear, a gray is the unit of absorbed energy, and 1 gray equals 1 Joule/kg. For comparison, CT scans work in the ~50 mGy range and radiation therapy in the ~50 Gy range. The bizarre thing is, if you're exposed to >5 Gy it's usually lethal. But that applies to usual radiation, gamma radiation. The effect of a proton beam is less known.
The protons in the beam can be accelerated up to ~70 GeV, which is 1/2000 of the LHC range. There's also the beam luminosity, which is a measure for the number of particles flying through a unit area per unit time. The LHC can reach 10^34 1/(cm^2 s^2) and the U-70 about 10^32 1/(cm^2 s^2). So the most naive estimate would be an increase of 10^3 - 10^5 of the radiation dose -- but that's more like an upper bound.
It won't destroy your hand or blast it off. But the effects of radiation are quite severe, and you will end up with a mutant hand.