The amount isn't 40 sa'ah, it's only 9 kav. From an IDF Q&A distributed by ShemaYisrael:
Q. How can a soldier who is on duty fulfill the custom of immersion in a
mikveh on Erev Yom Kippur?
A. ... The poskim write, however, that one who finds
immersion difficult can rely on fulfilling his obligation by pouring 9 kavim of water
on himself (depending upon various halachic opinions, that amount can range from
between 12.5 to 22 liters of water) in an uninterrupted flow that covers his entire
body. This is possible by showering.
That means 9 kav is ~3--6 gallons. Even a low-flow showerhead will use that much water in a 5 minute shower; of course how much of that water wound up on you? Make it a ten-minute shower and I think you're all set. I don't think there's any other special procedure, other than making the shower continuous (not turning it off to get the soap or something).