No, you should not put an egg, with or without the shell, directly into a toaster oven. Toaster ovens are not designed to cook eggs in their shells, and doing so can be dangerous.
Eggs have a high moisture content, and when heated inside the shell, the steam builds up pressure, causing the egg to explode. This can create a mess and potentially harm you or damage the toaster oven.
If you want to cook eggs in a toaster oven, you can do so by removing the shell and using an appropriate cookware like a small oven-safe dish or a muffin tin. For example, you can make baked eggs by cracking them into greased ramekins and seasoning them before baking in the toaster oven.
Always follow proper cooking guidelines and safety precautions when using kitchen appliances to avoid accidents and ensure your meals turn out delicious and safe to eat.