I highly DO NOT recomend using a pure BT release for hunting, there are a few that use them and seem to do well, but for me I find that a pure BT release in a hunting situation is far less than optimal......and I shoot a pure BT release for everything else.

What I would recomend is that you find a pure BT release that you like and then find a thumb trigger style that has a similar feel to the BT that you are using.
This allows you to shoot the pure BT release all year during practice, league, 3D, etc.....and work on getting rid of your target panic. Every once in awhile, slip in the thumb trigger release for a couple of shots just so you are comfortable with it.
When you head to the woods, bring the thumb trigger and leave the BT at home.

While I do try to use proper form and technique for every shot, sometimes in a hunting situation that just isn't going to happen, or you need to get a shot off quickly. The thumb trigger allows you to command shoot the release if push comes to shove.

The wrist strap is a good idea, as is putting a backup release in your pack. I have dropped my hand held from the tree a couple of times but have always had a backup up there with me.