Is there any way to get around this anti-static strap that's in the instructions for changing the card?
You can touch a metal part of the interior of the case to disperse static buildup. You may want to touch the metal part of the case periodically while you're installing the card, depending on how long you take, how dry the air is, whether you're sitting on a rug, whether the clothing you're wearing has a tendency to generate static, etc.