Then wash yourself in cold water. If you suddenly feel an urge to shave, buy a straight razor once and maintain it. Soap for personal washing is largely unnecessary; you can get by using only a small amount. For clothes, you only need to heat a limited amount of water, and you can wash by hand; again, soap is something you don't need to use a ton of.
During the water crisis here (we were rationed to to ~50 litres per person per day [this sounds like a lot; the average person can blow through it in minutes]) I had a colleague who cycled to work every day and took only extremely short cold showers every other day. His personal hygiene was fantastic (I sat in meetings in un-air-conditioned rooms in African summer heat with him, I should know).
It's entirely possible to live practically off-grid. You don't have to become a cave man. You can maintain the same standard of appearance and hygiene. It's just hard, tedious, unpleasant work.
I don't think you're unreasonable for not doing it, but I don't think you're being honest with yourself about your reason for not doing it.
E: I guess this fits pretty well into the die nobly/live humbly dichotomy, viz. it's easy to die for a cause, it's hard to live for it. You want to die nobly for your cause, but you're not willing to put in the hard yards to live humbly for your cause.