As a recent convert to cold water shaving, I wonder if the lack of the shower contributed to the success.

Shaving made easy; what the man who shaves ought to know .. : 20th century correspondence school, New York. [from old catalog] : Free Download & Streaming : Internet Archive. Go to pp. 50-52. It explains that you don't want the beard softened, but stiff, in order to get the optimum closeness and comfort.

I was a hot water shaver until making the switch a couple of months ago. I don't have a heavy beard and probably for me it doesn't really matter whether I use hot or cold. But for certain people, all things being equal, I think the cold water approach deserves your consideration if you have a problem. I have another motive for going cold. I had an electric water kettle, scuttles, and preceded the shave with a shower. Those things take time, and I don't have to fool with that stuff any more.

One of my personal shortcomings in life has been a tendency to overcomplicate things. Shaving has been no different. I am embarrassed by all the things I have tried when the answer for me was to keep it simple. If you are having trouble, try skipping the prep, whip up a good lather, and try going cold. Just try it and see if you can circumvent some of the elaborate preparations and arrive at your answer.