Which doesn't help if you assume the attacker has a dremel.

"Opening it with a dremel" is a completely different class of attacks from "opening it without leaving a trace".

Changing the lock code isn't really leaving without a trace.

If I open my hypothetical safe once a month, I may not find out that someone has changed the code for up to a month.

If someone cuts it open with a dremel, I'll notice as soon as I happen to see it.

Is it the same as taking a dremel to it?