You should be able to dry camp for 4 days easily. You just need to conserve water. You really don't need a shower every day. Wipe down with a wash cloth inbetween. Never leave it running for washing hands, teeth brushing, dishes or showers. Hand washing & showers: Wet down. Soap up. Fast rinse. Teeth brushing - you only need about 1/2 cup to complete. Dishes: You don't have to do them every day and only use about 8" of water. Grill outside and use paper plates. Vegetable pots or fry pans can be wiped out with a paper towel and reused.
Your batteries will require careful monitoring. Running a furnace will deplete them fast. Don't let it run overnight... bring extra blankets. Turn on for a short time first thing in the morning and a short time in the evening before bed. Use minimal lights. Get a stovetop perculator for coffee. Butter bread and plop it in a fry pan for excellent toast.
Remember... there are many tent campers or pop-ups that will have the same issues but will have less water and no electric.
If need be, there are public showers in Estes Park. Try to use them in the afternoon as it won't be the busy time. They're kept clean but wear flipflops while showering.
Enjoy your trip. You can do it!! Don't let this be your first and last experience without hookups. There are some beautiful campgrounds out there to stay if you're self-sufficient.
