Yes, you can set up Shopify so that it uses Cash on Delivery. Go to Settings > Payment and find it under "Manual Payments". You don't need to accept credit cards if you don't want to.
Also, check Aramex App here:
Hope this helps.
Cash on delivery can be enabled from the Shopify dashboard under Payments settings. For handling Aramex shipping, you can use the Multi-Carrier Shipping Label app, that will help you automate the complete shipping process.