These are factors I know of that play a role in the amount of shock you absorb from your axe handle, such as chopping style, grip, handle rigidity, cutting ability and wood type. These are the kinds of things that can allow a person cut more, longer and in harder wood without incurring numb sore hands, tendonitis, etc. More text below.
Chopping with an axe is a high impact, high energy exercise. As choppers, we necessarily absorb some of that energy since we are holding the tool. There are a number of factors I know of which are important in the cause or prevention of repetitive stress injury or discomfort in chopping, most of them at least partially controllable.
The axe should not be gripped very hard while chopping except as necessary in specific situations. A hard grip unavoidably tires and stresses the hands, but it also creates a more efficient transfer of the energy from the vibrating axe handle back into the hands. The Style of chopping is also important and interrelated to grip. A heavy handed chopping style should be avoided. Don't think of chopping as pushing or forcing the axe through the wood, but rather as whipping or throwing the axe head into the wood using the handle. Pushing on the handle after the axe hits the wood adds little if any real power to the cut, but stresses the handle and the hands and probably sacrifices control to some extent. You can cut plenty deep if you build velocity in the axe head before it hits the wood. If the work is done before the axe hits the wood, then the grip is only to lightly control the axe after it strikes.
The handle of the axe, depending on it's thickness, density, inherent flexibility of the wood and probably other factors, will transmit more or less shock. Thin handles transmit considerably less shock than thick ones do and tuning your handle or thinning it down is probably mentioned by authors writing about axes more often than not. Older axes tend to have thinner handles than modern axes, and vintage axes, old photographs and older illustrations demonstrate this fact. There is a reason that axe handles have become thicker, which is that they aren't actually used very much. Most axes are now the equivalent of handbags for men, and are put to real use only infrequently for short periods of time.
If you cut into wood at an angle, usually around 45 degrees, it cuts more easily than if the cut is made at a right angle. When cutting at 90 degrees the axe stops suddenly and more of the energy embodied in the head is transferred to your hands rather than cutting into the wood. It's fine to cut at 90 degrees as needed, but generally a poor habit to get into on a regular basis. Most axe work is done with cuts around 45 degrees for a reason.
Another way to transfer a lot of the energy embodied in an axe head back up the handle and into your hands is to use an axe that is not cutting well for any number of reasons. The axe must cut well and easily or it will stop suddenly causing more vibration. Most axes as they come from the factory, nearly all in fact, require at least some reshaping to get them cutting well. In most cases, a significant amount of metal needs to be removed from the sides of the axe near the bit in order for it to be able to slide easily into the wood. It is often recommended to file the cheek of an axe in a fan shape, but that depends on the shape of the axe head to start with.
Finally, the wood plays a role. When chopping hard dry wood, less of the energy from each blow of the axe is dissipated in cutting, whereas when cutting soft and green woods, the energy is dissipated gradually as the axe sinks deeply into the cut. You may or may not be able to control what wood you end up cutting, but you can control other factors that cause or prevent the kind of handle shock and fatigue that might keep you from working or cause a longer term injury that will put you off of work for a while. The stuff mentioned here is important if a person want's to be able to use an axe under varied conditions, on varied woods, for longer periods of time, on consecutive days. What separates the men from the boys isn't being tough enough, young enough or dumb enough to tolerate a club of a handle or an axe that otherwise doesn't cut well, but to be wise enough to work smart and not hard. If you are going to sit at your computer trying to breath life into your flaccid member to some freaky internet porn, or work your thumbs out pushing buttons on your t.v., remote then I guess maybe none of it matters all that much. If you're going to dig, carry, lift, hammer, weed, process and otherwise use your hands, wrists and arms, you'll be able to do all of it more, and longer, day after day if you pay attention to these types of details.