Maybe you could take a look at the Specialty line of peep sights. There are a couple versions, each using threaded inserts of different sizes. You could get a 3D set that includes all the inserts from 1/16" up to 3/16, I believe. As I said, there are a couple different models. This would allow you to just change the insert when going from insdie to outside.

The only thing I see about the peep you are looking at is that those cross hairs would just seem to block out available light and I don't know that having the peep so close to the eye would make those crosshairs all that visible anyway.

Of course, I could be wrong about it. Your eyes would certainly be younger than mine so may work well for you. You never know till you try.