How are you going to power it "externally"? Do you have an external adapter of some kind? Is it going to be installed in a motherboard and ONLY be externally powered for the PCI supplemental power but still receive it's slot power of 75w through the motherboard?
Or is it going to be installed in a completely external adapter housing and not in the motherboard at all?
Regardless, it's unlikely you will find an 8 pin or 6+2 pin connector on anything smaller than a 450w unit anyhow, so if the only thing that the PSU will be powering is the PCIe supplemental circuit on the graphics card, then a 450w unit used in conjunction with whatever is powering the rest of the system should be fine but you are going to need a special configuration adapter or manually power on the external PSU prior to starting up the rest of the system every time. Overall, it's a bad idea. It is a MUCH better idea to simply obtain a PSU that is capable enough, and of good enough quality, to run the whole system.
These kinds of "frankenmodifications" rarely work out the way people want them to and if you're simply trying to avoid purchasing one unit with enough power for the card plus the rest of the system, I would say it's not recommended that you do things that way.