Let's get some stuff straight so we're all on the same page:
 
nVidia wouldn't know what your system configuration is, so they make up a number since no two similar Wattage PSUs are alike anyway.  Thus, their "minimum system requirement" Watt and Amp ratings are not functional minimums, they exist for liability should your card malfunction, then EVGA Tech Support will scapegoat your PSU if it doesn't meet requirements as the source of the problem.
 
Fact is, a GTS450 at reference clocks consumes just under 9A from the 12 volt line (Max Graphics Card Power = 106W, where 75W is routed through PCIe slot and the rest via the single 6-pin).  Since you haven't told us your system configuration and I doubt you own a power meter to itemize, this number is altogether useless.  It seems stupid to change the PSU for 50W and 4A that you might not be using, but without knowing what your system is pulling now, you don't have a choice since the power supply isn't just powering the graphics card with everything plugged in to it.
 
Since only the CPU+GPU+any drives + any fans all draw power from 12v, all long as their total is less than your 18A max with some overhead (since running anything at peak reduces its operational life), then you're good to go using GTS450 with your 350W PSU.  But you have to do the math and research-- most folks don't have the patience for this (ironically, many enthusiasts included), hence they would rather go out and get a new PSU with overkill Wattage and Amperage for the false sense of confidence.
 
FYI, I've done the math and research already in response to many other similar questions people have asked on these forums as yours (i.e. GTX690 on a 650W unit, power needed for a pair of GTX690), and unless you own high-end components overclocked, your 350W unit is fine for your GTS450.  
 
But like I said, should anything ever go wrong with the card, you have to be able to explain to Tech Support why you don't have their minimum proper PSU; I could easily, but you have to back up claims that it's the card's fault.  Do your power supply homework and use the links I gave as a starting point.