Is there a usage of "the" that indicates one out of a group of many?

This is a specialised use of "the", which designates a typical or even stereotypical member of the set, not any particular member.

The definite article can be used, as in your examples, for what is known as ‘generic reference’, that is, a reference to a whole class of things rather than just one or more instances. However, the indefinite article, and the plural of the noun with no article, can also be used to the same effect. So your examples could, with the same meaning, be written as:

1a. A wise warrior stops a ranged attack before it nears him.

1b. Wise warriors stop a ranged attack before it nears them.

2a. Through judicious placement of wounds, a marksman ensures that his enemy cannot escape him.

2b.Through judicious placement of wounds, marksmen ensure that their enemy cannot escape them.

Not sure what 'a ranged attack' is, by the way.

This special use of the about a type of person, indicates that this kind of behaviour linked to that person is something that is important for that kind of person, and is probably the one thing that defines this sort of person.

Take your second example:

The wise warrior stops a ranged attack before it nears him.

This means that a warrior is not wise if he doesn't do this. It is the most important distinction that separates a wise warrior from any other not-so-wise warrior.

The other example:

Through judicious placement of wounds, the marksman ensures that his enemy cannot escape him.

means that this way of eliminating an enemy is the most important thing that defines a marksman.

As for your first example:

Nearly anything can be a weapon in a martial artist’s hands.

This is not really the core of what defines a martial artist, even it is something any good martial artist would be capable of.