When I graft, I use 1/2" green nursery tape. I start below the scion, wrap up over the graft site, until it is covered. That hold the scion in place. Then I wrap back downward, pulling it very tight, to press the two pieces into good contact with one another, and then tie the two ends together. That is enough.
The number of layers you have is too much, but if it is only over the graft point and the buds where growth will come from are not under the tape (just under the parafilm), you will be fine.
Yes, first rule of grafting is to know where the knife will go when it slips (and it will), and to make sure that you skin is not in the path. If the knife is sharp enough to cut the wood, it is definitely sharp enough to cut you.
For softer wood, and if you are not doing a lot of grafts, you can use an x-acto knife with a fresh blade. Otherwise get a knife made for grafting. It makes life simpler. There is a reason why grafting knives have been developed - because they have the right characteristics and simplify the process by their design and shape.