I know that charging stands (with special battery packs) are
available, but since the documentation specifically cautions
against in-situ charging, I am unsure if these would invalidate
the warranty. There certainly seem to be some tales of woe
amongst product reviews.

I have a cheapo charging stand for the kids Wii - the original controller
battery cover is replaced with the supplied battery pack with contacts on
the back if it's cover. Charges when placed in the stand. Has been in daily
use for over a year with now issues.