What is involved in issuing prepaid debit cards through offshore banks?

You will simply have to find an off-shore bank that is not only an issuer, but has the CMS (Card Management System) to handle pre-paid as well as is able to onboard customers from around the world (I’m presuming that would be your goal), in as little KYC/onboarding costs as possible.

The goal is to find someone who can do this and is comfortable with the low balances that might be maintained, has great network coverage and correspondent banking relationships to support the major currencies.

A good starting point is to ask your local VISA/Mastercard representative in your locale and ask them for recommendations and work your way from there.