If the wipe is damp and not soaked you will not need to concern yourself with it getting on circuit boards.
The only concern I have is whether or not it will damage the anti-scratch/protective coating on the phone. I know adhesives and removal chemicals pretty well because I have worked with them for years. While rubbing alcohol is a very mild solution I would still be concerned about it because the anti-scratch might be very sensitive. Why not ask a Verizon rep about what they recommend? Then if anything goes wrong demand that they replace the phone.
EDIT/Off-topic: Water itself is not an issue for damaging electronic componenents, but the impurities in the water can cause damage. I have seen a video of an overclocker running a PC fully submerged in purified water, but it is more common to submerge components in mineral oil.
And of course rubbing alcohol is not going to damage the system. It is highly recommended to use alcohol for wiping down the CPU and other components... it's not going to damage your phone any.