I've never seen a compressor shaft break or come apart. There is a metal keyway joining the two together. The 'click' you mention says everything is working on the front end. I doubt that that's the problem. Special tools are necessary to remove the clutch hub, pulley, and coil. You WILL ruin the compressor if you try using standard mechanics tool.
Before you start dismantling things and throwing parts at a problem and fall into a DIY money pit, a few more diagnostics are necessary.
Buy or borrow a REAL set of AC manifold gauges. This is a primary diagnostic tool. You can borrow a set for free from most autoparts chain stores for just a returnable deposit when returned.
The pressures with the compressor turning, AC on HIGH fan, windows open, engine running about 1200-1500 RPM will tell the story.
The system could be just very low on refrigerant. THe high side pressure will tell the story.
If it IS LOW, (most common problem) there is a slow leak in the system. Could be the front seal of the compressor. Look for oily residue sprayed on the hood above the compressor. Get a good look at the compressor shell and the bottom of the clutch area - is it covered by an oil slick?
Check all the other fittings and hose connections. The crimped hose connections DO wear out and leak. They will be covered with oil too.
Next thing to do would be to have the system refrigerant that is still in the system recovered, and then a full vacuum pulled on the system to see if it holds. If it does, then a total refrigerant recharge into the vacuum (by weight). Now the system can have a full diagnostic to see if everything is working correctly.
If the vacuum doesn't hold, then the source of the leak must be found and repaired first, or the recharge will just leak out and be wasted.
Do you plan on doing this work yourself?
Sometimes you just have to accept things at faith value!