When I was a kid we didn't have a shower, only a bath. There were four of us kids and my mum. The only way we had of heating water for a bath was by lighting a coal fire underneath a stone boiler, the hot water then circulated into a storage tank. To heat enough water for all of us to have a bath took all day. Coal was expensive, we were poor, there were frequent miners strikes, in summer it was too hot to light the fire. The point to this story is that until I was 18 and left home I never thought of it as normal to bath (or shower) every day, often just a lick with a flannel and soapy water was enough. Then this year when I had my bathroom refitted I didn't have a bath or a shower, I used baby wipes on the areas that mattered. I went 10 days like that without getting too smelly. I used dry shampoo on my hair just to stop it looking too greasy. As for shaving, well in my opinion it doesn't matter one way or the other.

Missing a shower for a few days doesn't really matter, missing a shower for a few weeks definitely does matter. You will feel a bit more comfortable in yourself if you do shower, it will be worth the effort even though the thought is intimidating.