Hello,
I am the owner of an american offshore company based in Delaware (est. 1994, Tax ID, Internet business). I am a non US resident, living abroad (therefore no SSN).
I am interested in a credit card and checking account in the US for this company, for easier handling of payments (secured card =fine with me). I have a personal (Visa)card for some years already. Company is in very good standing.
Any proposals?

I am not prepared to give you professional advice, however your post made me curious: why can't you simply use a debit-based account (i.e. open a bank account in the U.S. with your TAX ID and request a card that's linked to that account)?

Secured cards are usually not a good option because they have various fees.