If you don't want to permanently delete files from your external hard drive by moving them to Trash, you can try the following two methods.
Method 1: Using the keyboard shortcut. If you want to permanently delete files on Mac without moving them to Trash, you can select them and press Command + Option + Delete.
If you accidentally permanently delete your essential files, you can use iBoysoft Data Recovery for Mac to help you restore them, which is a powerful and professional data recovery tool to help you recover kinds of files on Mac/MacBook. It supports macOS Sonoma, macOS Ventura, etc., and Apple Silicon.