Superhunt, they now recommend against using a snakebite kit. There were so many incidents where people have cut too deep and did a bunch of damage to themselves or others cutting the bite area. The rest of your post is inline with what they now recommend. I have a brand new, meaning unused snake bite kit I keep because I haven't seen a new one for sale in years. I always had one in my backpack when I was a scout. They now recommend the below and to get to medical treatment asap. Telling someone who was bitten by a poisonous snake is going to be a pretty hard thin to do. Just one source of info regarding treatment of snake bites.

By Mayo Clinic Staff
Most North American snakes aren't dangerous to humans. Some exceptions include the rattlesnake, coral snake, water moccasin and copperhead. Their bites can be life-threatening.

If you are bitten by a venomous snake, call 911 or your local emergency number immediately, especially if the area changes color, begins to swell or is painful. Many hospitals stock antivenom drugs, which may help you.

If possible, take these steps while waiting for medical help:

Remain calm and move beyond the snake's striking distance.
Remove jewelry and tight clothing before you start to swell.
Position yourself, if possible, so that the bite is at or below the level of your heart.
Clean the wound, but don't flush it with water. Cover it with a clean, dry dressing.
Caution

Don't use a tourniquet or apply ice.
Don't cut the wound or attempt to remove the venom.
Don't drink caffeine or alcohol, which could speed the rate at which your body absorbs venom.
Don't try to capture the snake. Try to remember its color and shape so that you can describe it, which will help in your treatment.