Copying your words: (emphasis mine)
.... therefore I am required to inform them of all travel abroad.
So do that, inform them. As you mentioned, you don't need an approval, so just keep them informed about the travel. You can mention personal reasons as the purpose of the travel.
Whatever happens, don't lie.
Inform Employer About Job Interview
It is usually very bad idea to inform your current employer about ANY job interviews.
I was in a very similar situation, just that the government had nothing to do with my job. I told my employer that I am going to visit that country. After I returned, I took my time to think about the job offer. When I had the final ...