6. Use a Tampon to Stop the Bleeding
The cotton from the tampon can be used to cover or pack a wound. You will need to have tape on hand to affix the cotton to the afflicted area, but any good survival kit will have medical tape or duct tape in it already.
For a short trip into the woods, a single tampon and small roll of tape will be much easier to carry than a first aid kit. At the same time, you will not need to worry about being unable to pack or bandage a wound if anything happens.