I suggest you speak directly with the executor about this to find out why exactly he needs an SSN from you. My guess is that the inheritance may include stocks, bonds, or other investment property, and they may need a SSN in order to transfer the property into an account with your name. However, I believe what you actually need is an Individual Tax-Payer Identification Number, not an SSN - since you are a foreign national without a resident visa you can not get an SSN. See:
Obtaining an ITIN from Abroad