When i create a new menu item and set "Menu Item Type" to:
K2 » Item listings » Categories
and set only one category
I cant select another template, it is automatically set to the one that is defaulted to the category in the component

When I select more than one category, I can choose any template.

But I would like to choose one category and change its template.

You can change these settings from the category's parameters.
A single category's settings are set from the category's params.

I know that this is set in the category options.

But I wanted to create two menu items with the same category but different templats.

And if I only list one category in the menu item, then all other options are blocked. Options are available when I select more than one category..

So far I have solved it in such a way that I created a third position in the menu (not visible on the page), where there is one K2 category.
And in the two visible menu items I set two categories (one empty) and thus both can have different templates and single items open in the template of this first menu item with one category.

I hope that makes sense :)

This is actually the solution I was going to propose :)