Can short term exposure to cigarette smoke cause eye cancer?

Likely not. What kind of eye cancer you are referring here? Eye cancer is not common. I dont think that short term exposure to cigarette smoke can cause eye cancer. It may give you irrittation on the outside layer of the eye- conjunctivitis- makes your eyes red and discomfort. However, cigarette smoke is not something that you want to be exposed with, anyway-either as a first hand or as a second hand smoker.
Smoke gets in your. Eyes, is quite a classic song, but its the concentrated smoke that is inhaled that causes a variety of cancers. The inconsiderate side-stream smoke is obnoxious, smelly, and can literally sting your eyes and make them tear, but do not cause eye cancer.