Would a golfer say, "I shot for 200 yards"?

Solution 1:

To "Shoot for X" is an idiomatic expression meaning that you are trying to achieve a specific goal, X. Thus if the computer tells me "you shot for 200 yards", I would expect the follow-up to be "and came within 10 yards of it" or "but overshot by 50 yards" or some such measure of how successful I was at achieving the desired goal.

I doubt that this is your intended meaning, so I'd have to say that "You hit the shot 200 yards" or "Your drive went 200 yards" would be better expressions.

Solution 2:

Here are a few written instances showing that a golfer is often said to...

drive 200 yards
(or hit a 200 yard drive)

The past tense might sound slightly odd to non-golfers, but they drove 200 yards too. There wouldn't normally be a preposition though (for implies driving a car or golf cart/buggy).

Solution 3:

A golfer says "I shot a (score)". (Score) being their score for the round. They do not "shot" a distance. For that you can say:

I drove the ball about 200 yards today.

I had a drive (or shot but less common) that went 200 yards.

I hit the ball over 200 yards.