It affects the pins if you cut all the way through them. If you break the continuity at a point above the area that it makes electrical contact with the AGP slot when the card is properly seated, then that pin is disabled. Obviously, you don't have to worry about 3 and 11. You want them to be disabled anyway. But if continuity was broken in any of the adjacent pins, there would be a problem. If you want another set of eyes (or a bunch of sets of eyes), you can post a close-up picture of that section of the card. If a trace is broken, it can likely be repaired with some electrically conductive paint. A once popular example is the repair compound that comes in a nail polish type of container for automotive rear window defoggers (you'd actually just paint across the broken parts of the metal on the window). The same stuff can be used here, but with a toothpick instead of the included applicator brush. It's not as common as it used to be, but I think NAPA still carries it. Radio Shack carries something called the Circuit Writer Pen that is specifically designed for stuff like this, but it's pretty expensive for a one time use (about $20 or so).
I'm not very good with tape either. I only used it last week because I was flashing in my G4 for use in my G5. But I cut the tape to size before sticking it on the pins. It's no less tedious doing it this way, tweezers and magnifying glass were involved, but it seems less risky than using a blade on that area of the card.
I tend to go for the resistors for two reasons: As mentioned, I'm not very good with tape. I also tend to move things around a lot and I don't want to have to worry about tape when I'm swapping cards around. It actually happened once that some tape got stuck in the AGP slot and made it appear that my motherboard had failed. In your case, with the next card, I think maybe I would start with tape in order to verify that the card is recognized before making any permanent changes. If it acts as expected, though, I guess it would be pretty tempting to just go ahead and flash it and leave it the way it is. I see your dilemma. I don't think tape is normally dangerous, though. Just be sure to shut down and unplug the computer if you have to redo it.
It really would be nice if you had access to an AGP PC to test it with before making modifications. It's nice to know whether or not you're starting with a working card. And you can get your money back if it's not good. Once you start making modifications, you can't.