HSBC singapore does not require personal visits for personal accounts.
Standard Chartered Singapore asks for introduction by a current SC client, that's all. If you don't have one, then you might have to visit.
hsbc channel islands also does not require a personal visit, unless my info is no longer currrent.
Panama Legal is seeking a corporate bank account I am 99% sure as there is no privacy gained from personal bank accounts in today's environment of transparency in banking.
I would recommand FBME Ltd in Cyprus...check www.fbme.com
I will not try and sell the bank to you, but if it is what you are looking for, send me private message as I can get you introduced to the bank (require approved introducer).