word choice - What type of pronoun shoould I use before a gerund?

While reviewing grammar, I came upon this sentence:
"I was able to inspect the apartment without his noticing the movement of my eyes."

However, this phrasing seems awkward, especially the "his".
I feel like one of the following two changes would be more grammatical:

I was able to inspect the apartment without him noticing the movement of my eyes.

I was able to inspect the apartment without his noticing of the movement of my eyes.

Are either of these two more "correct"? Or are there any other better changes?