Electricity – As already stated, don’t use your starting battery for anything but starting the engine. If all you use your house battery for is lights and stereo, it will probably last the entire trip. (Don’t use a 12V coffee maker. Heat water on your stove.) Days are long now so if you go to bed when or shortly after it gets dark, you’re not going to consume very many amp hours. Having a LED anchor light and nav lights is a big plus. If you have an autopilot, it can be an energy hog. To conserve energy with cabin lighting, a small LED lantern can provide ambient light and LED headlamps can provide task lighting (such as for reading). With typical use, the three or four AA or AAA batteries they take will last way more than a week. I also carry a “jumpstart battery” on board as a backup source of power. I don’t know your itinerary or philosophy, but if it’s a typical Great Lakes cruise, you will probably be motoring some, which will recharge your house battery somewhat. Worse case, check your house battery once a day with a voltmeter and if necessary, run the engine to charge it a bit.
Water – I usually figure two gallons per day per person for drinking, cooking, and hygiene. Count your consumable beverages (e.g., beer, soft drinks) as part of your water allowance. If you have electrically pumped water at sinks, that can use a lot more water than necessary. I always carry a five gallon jug of water as a backup just in case something happens to the water in my water tank. When in fresh water, I also take the water filter I use for backpacking (MSR Miniworks) which provides another source of potable water in an emergency. If you end up going to a pumpout facility mid-trip, you should be able to top off you water tank at that time. As mentioned, use lake water in a solar shower or small garden pump/sprayer for a warm shower.
Waste – I have a 17 gallon holding tank and that is adequate for two people for at least 4-5 days. By being very judicious in the use of the toilet, your 25 gallon tank may be adequate for the entire trip. To be safe, get a list of marinas with pumpout facilities along your route. If necessary, you can just pull in (typically at the fuel dock), get your tank pumped out, top off your water, buy ice, then move on.
Refrigeration – It’s a convenience, not a necessity. There are lots of foods (canned, fresh, dehydrated) that will last a week without being refrigerated. I always take a couple of Mountain House meals as backups or for times when I want a no hassle, hot and fast meal. Canned or bottled drinks can be kept cool by storing them in a locker below the waterline or hanging them over the side in a mesh bag. (But if you do that, rinse off the top with potable water before opening and putting them to your mouth.) It may not be the diet you prefer, but it can meet your nutritional needs and, remember, it’s only for a week. Before the trip, experiment at home with meals made up of foods that don’t require refrigeration to discover what you like and to avoid unpleasant surprises.
Dinghy – The odds are that your Sevylor will do the job on most days of your cruise. In my early days of cruising (which was on the Great Lakes), I used something similar. If you are far from shore and/or it’s windy and choppy, you may have some difficulty. Otherwise, it should be adequate to get you to shore and back. Taking a repair kit would be advisable. It’s fairly lightweight so make sure you have some way to secure it when on shore so it doesn’t blow away. And I always put my wallet and other things I didn’t want to get wet in a dry bag tied to the “dinghy” so that if something went wrong, nothing important got wet. In my area, Walmart sells some inexpensive but decent dry bags (a package of three dry bags of various sizes for $10).
Anchors – I always take at least two anchors – a working anchor and storm anchor suitable for the bottom conditions I expect to encounter. I currently use all chain rodes but for a long time I used a chain-nylon rode (25-30 feet of chain) in the Great Lakes and had no problem.
Clothing – Most of my cruising recently has been on Lakes Huron and Michigan. They are cold enough that even in mid-summer there have been times I’ve had to wear winter clothing to keep warm. Lake Erie is warmer, but I would still take some real warm clothes (coat, watch cap, gloves) just in case. (No one believes me when I tell them it gets COLD on the Great Lakes at night, even in summer. Two weeks ago I did an eight day cruise and there were times I was wearing four layers on top, including a down jacket, long underwear, a watch cap, and gloves. Water temp was 38*F. Now it's up to 50*F.)
Dockage – I’ve only cruised Lake Erie twice, the most recent time was eight years ago. That was during the summer and the only time I couldn’t get a transient slip when I wanted one was when I stopped at Put-In-Bay during its Christmas in July celebration. Maybe times have changed or you’ll be hitting popular destinations at peak times. But I wouldn’t assume that no transient slips will be available.