I am going to shoot video of me standing at a mark the entire time with very slight head movement looking either left or right. Here is an example of the style that I am trying to replicate. http://revision3.com/diggreel/steaming/
1. Would using a Sennheiser K6/K6P mic hanging from a c-stand arm work well for this?
2. Are there any issues with using gaffer tape to tape the part of the mic where the XLR connects to it to the c-stand arm?
The only issue that might affect you would be any vibrations transmitted to the mic as you're not using a shock mount. That said, in a pinch, I've used a mafer clamp to GENTLY hold the mic. It allows you to point the mic fairly easily, too.
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I think you'll be OK. Play REALLY CLOSE attention to where and how the mic is pointed.
Use G-tape to make a little cradle or sling for the mic and that will answer John's good comment about vibration.
A/B the lav and shotgun to make sure the shotgun is what you want. I'm not a big fan of the K6.
Sometimes a lav can work better than a shotgun in a shot where the space is a little slappy. Just don't hit yourself in the chest (and mic).
If the shotguns does hear too much room, you can always hang some blankets around yourself just out of frame to reduce the bounce. Don't forget to put one on the floor.
BTW, the mic of choice (unless you're on an acoustically designed set would not be a shotgun, it would be a hyper or super cardioid. To hear why, download this.(warning: 22MB). You'll see a Quicktime logo on the screen until it downloads. Listen with headphones!!!