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Yes you can send in a paper form. I was able to find this online application which I believe you can print out and mail in.
Also there is this from the Delaware Unemployment FAQ page:
How do you apply for unemployment insurance if you currently don’t have internet access?
We accept Unemployment Insurance applications outside each location. They can be returned by mail or dropped off at our secure drop box outside our Wilmington and Dover locations. Self applications must be completed in full and must be legible.
Mail: Division of Unemployment Insurance PO Box 9950 Wilmington, DE 19809-9959