I'm not quite sure if you mean the PSU is too big for the case, or too small.
If the PSU is too small you should be able to get at least 2 screws in place - HP uses it's own proprietary PSU in most of it's PCs so you don't buy non HP ones later on. But even with two screws in place you'd be fine as long as you don't move the PC around much.
Try the different screw holes and see if you can't get another screw in at the same time. I've worked with 3 HPs here at work and used the standard ATX PSU with them, as well as other forum users over the past few months.
If your PSU doesn't get the 2nd screw in place you might be stuck calling HP to see if they can't provide you with a higher powered PSU.
I'm thinking about taking off the shell of my old PSU (I know that capacitors can shock/kill me, lol) & just hiding the smaller one in it.
If it's not plugged in you'd be fine to pull it apart...but I doubt you'd be able to hide the new one in the old one's case. It almost sounds like the best thing you could do would be to get some brackets made up. I don't know about the costs, but getting a piece of metal cut with a hole for your new PSU to stick out and screw holes to install it into your case would work. I get work like that done for work, but it's usually in large orders.
Have you given HP a call to see if they have larger wattage PSUs?
And try to fit the HP components inside, at the very most you may have to buy a new mobo, but the rest you can bring over, HDDs, CPU, RAM etc etc, and at least you have a case & PSU thats future proof then.