I worry that Biden, with access to the nukes and other security issues is at risk

The nuclear button isn't a literal button. There's a bunch of layers between the President and the actual execution of a nuclear strike.

I would consider a more pressing issue that you've got people climbing the ranks that really don't think using a weapon would be so bad. And a gradient that encourages a certain kind of officer, who would sit in the room with a senile President and encourage him to take the most drastic approach.

But that's less a senile old man issue. Worked just as well on young guys like Obama and Clinton as it did old-heads like Trump and Biden.

He and Trump are both not suitable to be President

Given the state of the executive branch and the methods by which Presidents only seem capable of pointing at places on a map and ordering them demolished, I'm not really clear who IS suitable. The best you can hope for is a peacenik President. And that only saves you for four to eight years, before the next guy comes in promising to make up for lost bombings.