While I want to learn celestial nav just for the heck of it, having a backup handheld GPS or two is pretty inexpensive these days. Now that basic GPS units have fallen below the $100 mark, it's hard to have an excuse NOT to have one for a backup.
However, access to the satellites themselves does pose a single-point-of-failure issue, and you need the batteries
or external power to keep it running. The risk and likelihood of a failure (or disruption) is pretty low, but it is there...
As far as an updated reference for Henderson's book, pretty much everything else in it is still relevant these days, if I recall