There's a flow in your logic there.
Since you are drawing a "C", the "path" should be an array containing the x,y positionf of the mouse during the path was drawn, not just the starting point and the ending point.
So it seems to me you should put up some "record" system, that will keep in memory the points where the mouse went by and THEN move the sprite from positions to positions until it reaches the end point.
That would be for a case where you first draw your path and then move the sprite.
If the sprite is to follow the path as it is drawn, then every X sec, set the sprite position to the current mouse/touch position.
Depending on the interval X, the movement can be more or less precise.
To know about sprite movements, check this topic