The answer to your question can be found in Rule 26-1. The relevant portion of that Rule is pasted below. The two relief procedures are alternatives to playing the ball as it lies in the water hazard, without penalty. Two additional relief options would be available if the ball came to rest in a lateral water hazard (marked red). If you have access to the 2008-2009 Decisions on the Rules of Golf, a very nice diagram of the alternatives can be found in Decision 26-1/15. By Rule, you are not allowed to take relief on the putting green side of the water hazard in the situation you have described. By taking such relief, you would be exposing yourself to further penalty, including the possibility of disqualification. (See Decision 26-1/11.)

Rule 26-1. Relief for Ball in Water Hazard. It is a question of fact whether a ball that has not been found after having been struck toward a water hazard is in the hazard. In order to apply this Rule, it must be known or virtually certain that the ball is in the hazard. In the absence of such knowledge or certainty, the player must proceed under Rule 27-1.

If a ball is in a water hazard or if it is known or virtually certain that a ball that has not been found is in a water hazard (whether the ball lies in water or not), the player may under penalty of one stroke:

a. Play a ball as nearly as possible at the spot from which the original ball was last played (see Rule 20-5); or

b. Drop a ball behind the water hazard, keeping the point at which the original ball last crossed the margin of the water hazard directly between the hole and the spot on which the ball is dropped, with no limit to how far behind the water hazard the ball may be dropped.

Although it is not advised to use lift, clean and place, the following veribage is suggested by the USGA if you do use it:

If a player’s ball lies on a closely-mown area through the green, the player may mark, lift and clean his ball without penalty. Before lifting, he must mark the position of the ball. The player must then place the ball on a spot within six inches of and not nearer the hole than where it originally lay, that is not in a hazard or on a putting green.

A player may place his ball only once, and it is in play when it has been placed(Rule 20-4). If the ball fails to come to rest on the spot on which is was placed, Rule 20-3d applies. If the ball when placed comes to rest on the spot on which it was placed and it subsequently moves, there is no penalty and the ball must be played as it lies, unless the provisions of any other Rule apply.

If the player fails to mark the position of the ball before lifting it or moves the ball in any other manner, such as rolling it with a club, he incurs a penalty of one stroke.

PENALTY FOR BREACH OF LOCAL RULE:
Match play – Loss of hole; Stroke play – Two strokes.
*If a player incurs the general penalty for a breach of this Local Rule, no additional penalty under the Local Rule is applied.

Hopefully this answers any questions.

Jimmy Becker
Assistant Director of Rules & Competitions