Geena, The reason they say that is because the winding wires have a lacquer coating that you cant solder to, and which is extremely difficult to remove**. So if you cut off the pre-solder tinned end of the wire you have a very big problem soldering the bullets back on, hence the 'irreparable damaged' comment.
However providing you only trim a few mm off the end retaining enough of the solder tinned part to allow a good solder joint it does no harm at all. Soldering problems aside, actually shortening the wires in itself is not a problem. In fact the shorter you can make the wires the better, as it reduces resistive losses (not that the difference is big enough to notice)
Having said all of this, for the little bit of exposed wire shown in the pics above I'd not bother trimming, I'd just put heatshrink over it, like you suggested.
**The only reliable way I've found of stripping the lacquer is (with single thick strand windings) by scraping it off with a scalpel or sanding off with sandpaper. For multi strand windings it is much harder, only way I've found is using boiling caustic soda and salt mixture, which strips the lacquer off instantly but is very dangerous.