Craig:
It will be a lot like camping, but GO FOR IT!!!
Your DC amphour consumption will be low, maybe 20 amphours a day. Run your propulsion engine for an hour or so if the house battery voltage drops below 12.0 volts at rest. You probably don't have an external regulated, high output alternator, so just run the engine to put back a days worth of amphours. Don't try to fully charge.
With fresh water under your keel you may not need your on board supply for showers. My wife and I made it on 5 gallons per day in the Bahamas for months with quick showers, quick dish washing and some for cooking and drinking. Well, maybe not drinking. Take along a couple of 5 gallon water jugs just in case.
The only upgrade I would consider is your anchor and rode. Your boat sounds like it is in the 30-35', 10,000 lb range. You need at least a 30 lb Delta, CQR, Rocna or Manson Supreme, the latter two would be my preference. And you need at least 50' of chain and enough nylon to give you 6:1 inclusive of your bow roller height.
Such minimalist weeklong cruising will either inspire you for more and lead to upgrades in water and electrical capability or maybe you decide it isn't for you. But do it and see.
David