This is a great question, thank you! There are a few differences between the use of alexandrite and diode lasers for hair removal. Diode lasers performs on a longer wavelength with deeper penetration. Longer wavelengths help avoid skin damage superficially in darker skin patients and performs well on coarser hair. Alexandrite operates on a shorter wavelength, which is more effective for lighter skin types. While both lasers perform well, and have had successful results, it is best to consult with your laser practitioner and physician to figure out which is the best for you. With you wanting to target just your cheeks, and taking into consideration your olive skin tone, you may do well with Alexandrite if your skin is light enough but in my practice I use the diode because it has great efficiency but is safer (but still effective) in darker skin types.   

Says Frank Andrewson M.D.