I'm afraid to use hotair on SMD can style caps. The value will no doubt be the same as all thee others near it, it's just an output or input rail filter/storage cap.
It would probably run without it too, but the more the better. And the size won't matter too much, as long as it's no big amount smaller that rest of them. You could probably salvage something similar off a mobo, or cablebox, or even a printer. Just make sure it's rated high enough voltage. Those are probably low ESR caps tho, on the GPU.
If you have the time, use a DMM and find what voltage rail it's attached too. Some rails only have 1-2-a few caps, so yeah, you can't always get away with assuming it won't matter.
With flux and copper braid, I'd clean the old solder off the PCB, and then tin/clean the replacement, and then tin the PCB and you should have enough metal showing on either end, to tack it down/reflow it.