Hi Griz,
The pump looks similar to the FloJet pump that I've got as part of my Glind shower setup. If it's anywhere near as good, it'll be a ripper of a pump. I would guess that the 80psi comes from the trigger nozzle. I would imagine if you did as you are saying and replaced the trigger with an on/off showerhead, that you could make yourself a perfectly functional portable shower.
This is the Glind shower rose, which I've pulled apart and siliconed up the inner two rings of holes to turn into a water-saving shower head:
http://www.glind.com.au/index.php/Accessories/11-Glind-Shower-Rose-+-Hose.html
If I were you though, for that money I'd be tempted to buy a proper FloJet pump from Ebay:
http://cgi.ebay.com.au/Flojet-Pump-Caravan-RV-/350418582447?pt=Caravan_Parts_Accessories&hash=item5196933baf
Sure - you don't get the case, hose and other bits with it, but you do get a high quality pump that you can get parts for and that you know will last you a lifetime. The rest of the stuff is pretty cheap and you can make yourself. Buy a cheap toolbox/tackle box to mount the pump in, an electrical quick-disconnect plug and some hose, and away you go. Especially since you're changing the showerhead anyway.
Good luck with whatever you decide - I'll be interested to see what you come up with!
Matto