I tend to remove all the tendons, but I am not really picky about silverskin when I am going to grind. I quit grinding shanks after I saw a recipe for slowly braising them. Its great meat when you cook them low and slow.
Combo of the two.
I am very particular about my meat, so it took me quite a bit of time when I was learning. Now that I've done ~40 animals, i have gotten a lot quicker, and figured out which of my knives work best for the job. Sharp knives will save you lots of time, and make the whole process easier. And to get faster, a lot of it is just experience.
For the shanks, I cut the tendon where it is mostly surrounded by meat. If its JUST tendon, I cut it. It'll just be chewy and hard once cooked, and no one wants that.
Otherwise, I remove tendons, glands, fat, hair, blood, etc. This really is the most time consuming part. Silver skin I remove if its easy and convenient. If not, I don't worry about it- it doesn't hurt anything. For the flanks behind the shoulder, same thing- silver skin removed if easy, otherwise left on there, and only big chunks of fat are removed. The white stuff throughout the meat is left.
It usually takes too long to process a deer myself when alone (I don't like standing at the counter for 3-4 hours), so I double bag all the meat I am going to grind and freeze it. When I am ready to grind (1-2 weeks later), I thaw it for 2 days in a partially open cooler, rotating it every 12 hours to get it thawed all around. Meat grinds A LOT better when it is partially frozen. Don't let it totally thaw.
For a deer, it takes me between 1-2 hours to debone, cut, package all my steaks, separate all the meat I will grind, and clean up. In the beginning it used to take me 2-3 hours just to debone a deer. When it comes time for grinding, takes me an additional 1-2 hours to grind, package, and clean- depending on how much I have to grind.
Personally, I add ~2-3% pork fat with all my wild game except wild hog. I add beef fat to hog burger. Most grocery stores with a butcher will give you fat for free, or sell it for relatively cheap. Just have to ask.
Processing takes time, and my guess is the guys that can do it quicker aren't as particular with the cleanliness, how it looks, or just have a LOT more experience.