If you did the calculations you're awesome!
The main danger that remains is dust. Dust particles reflect sunlight and can cause a huge change in climate. When a huge volcano erupted in the XIX. century, the winter after it were especially cold(I don't remember the name but I'm 100% sure it's not BS).
There were two big eruptions that century Tambora in 1815 and Krakatoa in 1883
The explosion would be similar in size to Tambora but since the sulfur dioxide released likely would be much less the global effects would be closer to Krakatoa.
Not an extinction event but could cause chaotic weather patterns and failed crops in some regions along with several years of unusually harsh winters.
The good news considering the size of the object and the lead time even giving a good shove with a VASIMR propulsion stage or attaching a solar sail should be enough to deflect it off course.
Even the propulsive capacity of a fueled chemical EDS might be enough delta V.
There should be no need for anything drastic like using a nuke.