To replace signatories? A company IS the customer at a bank, not the signatory. The signatory has no authority to bind the company. He is simply a signatory for a transactional account. A corporate resolution with meeting minutes copy directing the replacement of one signatory for another is lawfully sufficient paperwork to withdraw one signatory and replace another. The signatory would have no say in this process. Again the signatory is not a CEO, is not a Director... if the offshore structure is properly done... and does not have any say in how long he may remain as a signatory on the account.
If work for coca-cola and you are a signatory on an account, no bank has the legal authority to refuse replacement of the signatory, whether dead or alive. This is spelled out in a Banking resolution which is delivered and requested of Banking institutions at the time of the opening of the account.
But as anyone who is a lawyer or has opened offshore bank account before would know, banks rarely follow their own laws because they are so ignorant of private law vs public law. So if a bank truly is demanding a affidavit from the signatory (this still does not make legal since) then find a notary who will allow you to notarize a replacement order/agreement and leave the dates blank (including the notary date)
EDIT: And you if cant find a notary who will do this (many of them get sticks up their butt as if they are a higher authority) then pay for a homeless man to take the class and pay him to notarize your document. If you tenderly handled the relationship with the homeless man than he will be useful for future endeavors.