That is a decidedly bad idea on many levels. There is no reason at all in this day and age to do that.
Given the level of knowledge about PHP configuration evidenced in your post, what makes you feel that you are qualified to evaluate the potential amount of "damage" that this "web app" could do if exploited?
No, your web app does not "have to use fopen" with url wrappers. Your not being "inclined" to recode it in cURL, or use other methodologies to produce robust and reasonably secure code, is not a sufficient reason to unnecessarily subject the server you share with others to security risks that could impact the server or your neighbors who share it. It would be different if you were only placing yourself at risk, like on your own machine or a dedicated box that you alone use.
Then you might consider asking for help with that, or for suggestions for "best practice" alternatives that you can implement.
This indicates to me that you don't know nearly enough, or understand the ramifications of what you are doing sufficiently, to be "rebuilding" PHP for use in a production environment. To encourage you in this by telling you "how to do it" would be a bit like telling a manic depressive heroin addict how to obtain and load a handgun, and anyone who would do that is just not acting responsibly.
All the information you need to do that anyway, in spite of how foolish it would be for you to do so, is readily available on the net and in DreamHost's own wiki. If you researched the subject at least thoroughly enough enough to know the risks of what you are trying to do, there is always the hope that you would change your mind and not do it at all .... and if not, then you would at least know the answer to your question and not be here soliciting others to help you do it.
Harsh? Maybe, but seriously: Just because you can do something does not mean that you should do it - and this is one of those times that you should "just say no".
If you'll provide more details about what this "web app" does, and what you need it for (maybe even link to the app itself) so others could help you evaluate "safe" ways to accomplish the same thing, or maybe even help you "fix" it, I'll bet you will find those here that are more than willing to help you with that approach!
--DreamHost Tech Support