Some seller put the connector requirements is 6pin and 4pin and some put 6pin. I don't know which one is true. The Corsair GS600 only have 2x6+2-pin power connector, it does not have 4pin. And the HD 6750 is not listed in the Product Supported on AMD site.
The XFX radeon 6750 will run without any problem with you GS600, which has 2x6+2-pin PCI-E connectors. The 6750 needs one 6-pin PCI-E connectors, which is readily available with your Power supply, just split the 2-pin from the 8-pin, then you should have 6-pin connectors, Plug it. Your PSU amperage and wattage is totally enough for a 6970, let alone 6750... Even in the AMD website it says, it needs "450 Watt or greater power supply with one 75W 6-pin PCI Express" and of course, totally compatible with your GS600. I don't know what's up with AMD not writing the HD 6750 in the GS600 section on their website, but it should be totally compatible except you have problems with your PSU. Also, do not trust people that says you need 4-pin, because there are no such PCI-E graphic cards that needs to 4-pin. Graphic cards now need either 6-pin or 8-pin (Most PSU has 6+2-pin, but somewhere when I was browsing thermaltake's website for their PSU, they have whole 8-pin, but don't worry much about that, your's one doesn't) PCI-E connectors whether two of them or one. I don't know of graphic cards in the past have used 4-pin, but not with the Radeon HD 6xxx series which is in your case.
Go ahead and good luck on your buy , what a long typing lol.