That cable will work fine. I had a monitor that only had DVI and VGA inputs so i picked up one of those cables since my GPU only had one DVI and an HDMI and the other DVI was already in use. Since HDMI and DVI carry the same video signal you can use a cable like that and no conversion is required.
Cheers for your help and advice.....I was pretty sure they both carried the same kind of digital signal (minus the sound with DVI) but wanted to double check before buying yet another lead!!!!