Does the Delaware LLC need a resale license to sell online to customers in other states of America?

Hello,
Need an advice.
We are foreigners who have registered an LLC company in Delaware and we do have EIN. We are planning to do an e-commerce business in USA (online shop) with the help of drop shipping suppliers.
Normally, companies who offer drop shipping services do ask for valid Resale License or Tax ID registered in applicant's local state or country. But Delaware does not assess a sales tax on consumers, therefore there is no state issued reseller permit. (from the state website: "There are no state or local sales taxes in Delaware and as such, sales tax exemption certificates and reseller certificates are not applicable to Delaware.")
As I understand, it means that we do not need a resale license for online retail business in Delaware.
THE MAIN QUESTION IS:
Is it the same even if we sell goods online for customers all over the USA (not only in Delaware state)? We still do not need to obtain a resale license in this case?
Thanks for your answers.