Offshore Bank Accounts

Can You just open the bank account for my offshore company without me signing anything?

Almost, but not completely so. The client (the beneficial owner of the offshore company) is at least supposed to confirm to the bank that he is the actual beneficial owner. The bank would have a special form for that. In addition to signing that form, the owner would also be required to provide his due diligence documentation to the bank - much the same as was provided to the Registered Agent at the time of incorporation.