It would be very risky. Your system may reach the full capacity of the psu. Most people are saying that the 7750 will work on a 250w psu since it uses 75w max but it is not recommended. Please note that some 7750 models uses more power.
I would get a new PS....HP often comes with 250-300 watt Bestec AKA Worstec. I am getting an Antec VP-450 to replace my 300 watt Bestec on my HP. It's typically priced below $40....mine was $39 plus tax with free shipping from Newegg.ca
The Builder series is the value oriented line frm Corsair, but they are decent quality PSUs from a good, customer friendly company and are a great price-performance buy. You're not going to find a better PSU in the price range of the CX430 at $25. Who told you to stay away from the Builder series and what was their reasoning?
The Builder series isn't a top-tier PSU and it's not designed to be. The only issue that Johnnyguru had with it was the build quality...primarily soldering: http://www.jonnyguru.com/modules.php?name=NDReviews&op=...
It is arguably the value-king especially when it's $20 after discount/MIR. Despite the potential for some sub-par soldering it is still an exceptional value for $20.