You can probably apply with all the docs that you have and an explaination why you do not have reference letters and also an affidavit regarding your duties. Accounts has mentioned in on eof his post that he succeded with the affidavit
If you have no way out then I think it is no harm trying with affidavits
But V/O or I/O has the discretion of accepting it or not..
I suggest, if you are working in renowned organisations, then go for Affidavit, otherwise try to get it from your co.