Can isopropyl alcohol vapor damage polymers?
I will use your example of the mouse pad to answer your more general question.  

As you implied in your question, the mouse pad will be exposed to some isopropyl alcohol vapor if it is used to clean in the vicinity of the pad. As the vapor will quickly disperse to negligible levels, a simple solution could be to move the mouse pad (or other rubber-based or otherwise isopropyl alcohol sensitive item) to the other side of the room while cleaning the area around the computer. Once the area is dry and the smell is gone, there should be negligible isopropyl alcohol vapor remaining and you can put the mouse pad back. For the reasons discussed below, even this much effort is likely overkill and you can probably safely just clean around the pad and other items with isopropyl alcohol.  

The key reason that isopropyl alcohol vapors are much less damaging to the rubber component of the mouse pad is simply how much more of the compound comes into contact with the rubber when in direct contact with the liquid phase vs secondary exposure via the vapor phase. Depending on a number of factors (contact time with the liquid, temperature of the surfaces that are cleaned with the isopropyl alcohol, proximity and quantity of liquid used in vicinity of mouse pad, etc.) the mouse pad could be exposed to a few orders of magnitude more isopropyl alcohol when in contact with the solution than when merely exposed to vapors from cleaning some area in the vicinity of the mouse pad. This means that the exposure of the sensitive items to the isopropyl alcohol vapor is very small and not likely to have any noticeable effects on the exposed items like the mouse pad.