Question about purging carboy with co2

Ok, so I have an IPA that I am dry hopping in the secondary. I wanted to do a 2nd dry hop addition like Vinnie Cilurzo reccomends in the latest zymurgy edition. Here is my issue...

I've got a fair amount of headspace in my seconday and I don't want to oxidize my beer when I open the top (I use a carboy cap) to add the 2nd dosing of hops.

So, I was wondering if it would help, after I drop the hops in, to take off that white cap and hook a co2 line up to the spout, blow some gas into the spout and through the airlock, then cap it quickly. Or is there a better way to do this???

To me, not worth it. You're not going to get that much exposure when adding your hops.

CO2 is heavier than air, so very little oxygen will get into your carboy.

Doesn't seem necessary. You'll get for more oxygen coming from the hops as they soak in then you'll get from taking the top off the fermentor.