Shore power/ battery question

If you have a charger (converter) than "hums", it is most likely a ferro-resonant type, really not intended to be left plugged in for long periods. Just long enough to fully charge the battery, maybe 8 hours or so. A newer charger will be three stage: start at constant (usually maximum available) current until the absorption voltage is reached (around 14.4 on a flooded lead acid), then switch to constant voltage until the charge current goes down to a low value ( a few percent of AH capacity), then switch to a float voltage high enough to keep it charged but low enough not to evaporate all the water (around 13.2 for flooded cells). The older type that hums does not charge your battery very fast, does not stop once its charged, and makes annoying sounds.

If as you say you rarely use the charger/converter, just plug it it the night before the trip, save the money, and check your battery water every once in awhile.