Application of color to indicate interactivity in a table with a mix of sortable and unsortable columns

I'm working on an application and utilizing a blue color to indicate interaction. Links are indicated with the blue color and an underline, the buttons have a blue background, tooltip icons have a blue background, etc.

My question is: How do I apply color to indicate interactivity to table headers in a table with a mix of sortable(interactive) and unsortable(not interactive) columns?

I have thought of three approaches to this:

Keep the sortable headers blue and the unsortable black. Drawback: Column headers are traditionally the same color so having some blue and some black breaks from the norm. This would mostly look weird I think.

Keep the headers all black. Drawback: The expectation is set with the blue color as interactive, so leaving the headers all black could leave users thinking that they can't sort by the header.

Keep the headers all blue. Drawback: Completely misleading and seems like it could be the most confusing so I'm not even really considering this.