Vinegar is said to be safe to use for cleaning your laptop screen. Do not use it full strenght. Make a solution of 1 part white vinegar and 1 part distilled or dionized water. Do not use tap water or mineral water, either one could leave white marks on your screen. Be sure to use a non-rugged microfiber cloth or a soft cotton cloth.
You can also use iso-propyl alcohol using same solution measurements.
Put your solution in a spray bottle and lightly spray your cloth. Do not oversaturate it. Be sure to lightly wipe screen. If you apply too much pressure you may damage your screen. Hope this is helpful.