Should a button with a dropdown always have a click action?

I have one button that offers the user up to ~10 choices. The button label says 'apply as' and the dropdown lists all the possible choices. I have multiple choices on how to design this.

As a hover, where the dropdown opens on hover. As a onClick, where the dropdown opens on click.

I think I will be going for the hover as it is most commonly used, however should the 'apply as' also be clickable in that case? I dont have anywhere where the user should go as they need to define their choice first. It feels wrong to have a button that is not actually clickable, but only function as a placeholder for the dropdown.

Whats your opinion / advice?

Mockup: