Wafer-thin ice, as explained, is very thin, almost transparent. Does it mean very little chance? Definitely. It's ghost of a chance that Aunt Marilyn will come to the wedding.
I believe that when Monica says "wafer thin ice" she means Chandler is hanging by a thread because he is obssessing over the cousin. He asked if the aunt was going to the wedding because she said the cousin looks exactly like Aunt Marilyn!
Anonymous must be a big Friends fan...I was able to find a http://www.geocities.com/Hollywood/9151/719.htmthat includes your quote (is there anything that's not on the Internet?) and yes, the ice here is the kind you stand, or step, on, risking falling in.
yes, i think, you are correct, Monica was trying to say that their wedding is on thin ice (susceptible to call-off) and getting thinner e.g. "wafer" by Chandler's mischiefs.