In order to do this you will need an external program that can edit your .cdb file. The original program that many people still use is called SQLite; however, I personally prefer working with DataEditorX. I don't remember where to download either of these, though, as it's been years since I've first installed them, but once you have such an editor the process is very straightforward. I'll include tutorials for both programs.
1. MAKE A BACKUP COPY OF YOUR YGOPRO FOLDER. You don't want to risk screwing something up and losing your game's functionality, especially if you're doing this for the first time.
2. Inside the folder you want to customize, right-click on your "system.conf" file and open it in Notepad. At the bottom where it says "ignore_instant_updates", make sure that line is equal to either 1 or 2. If it's set to 0, then the game will just overwrite all of your changes as soon as you open it while connected to the internet.
3. Double-click on your "cards.cdb" file, BUT make sure YGOPro is closed before doing so. If it's open, the game will crash and you'll lose any decks you haven't saved.
4. On the left side banner, select the "texts" tab under the "cards" drop-down. This should bring up all the cards in your game, organized by setcode.
5. Scroll down on the right until you find the setcode of the card you wish to delete, then either right-click it and choose "Delete selected record" or left-click it and press the Delete key. You'll be prompted for verification, but after that the card will be gone from your card list.
6. When you're done, be sure to close SQLite before opening YGOPro again.
3. Run DataEditor, but make sure YGOPro is closed before doing so. This program doesn't make YGOPro crash like SQLite does, but none of the changes you make in here will be visible until you close and reopen YGOPro anyway, so just save yourself the trouble.
4. Open your "cards.cdb" file in DataEditor. You can either go to the File menu at the top, or simply use the hotkey Ctrl+O. All the cards in your game should appear in a list at the left. You can search for the card you're looking for by typing its name in the text box above the card's picture, then pressing Enter.
5. Select the card on the left that you wish you delete. At the bottom-right corner, press the button marked "Delete" in red. You'll be prompted for verification, but after that the card will be gone from your card list.
Hope this helps!