Ha! That's funny because I already removed the shroud for better cooling and to get at the fan (to get the part numbs, etc. )
I'll give that a go If I can find the right size fan laying around here....
I have a better solution. What I did with a 4770 and a 6870 when the fans died, is I took off the plastic shroud (you have to take the whole cooler off) and then reattach the heatsink without the fan, so it's just a big heatsink. Then you can zip-tie an 80mm or 92mm fan to it, and you'll find the card runs at like 50 degrees now, total upgrade! And it doesn't cost anything!
I don't think that's the right fan? That looks like a reference one.
Absolutely Wrong Fan. The pics I sent are identical to the fan I pulled off the card.