Decent Small Midrange WP8 phone?

Hi MS tribe,

I am looking for suggestions for a decent Windows phone with as small footprint as possible. It is meant as a replacement phone for a Luddite who owns currently a SGS4 mini, but is refractory to using Google's services (not because of ideology or fear, but because of complete lack of interest in technology). The person is also quite invested in MS services (Outlook mail, Skype), so WP should be a good match.

The ideal phone would be narrower than 65 mm, lighter than 120g, have a good battery life and good camera. Looking for a non-subsidized midrange device, not something that would break the bank ($400 absolute maximum).

App availability is a complete non-issue, but the option should be there, therefore a feature phone doesn't cut it. I could give Moto G, the aforementioned SGS4 mini as well as other "mini" variants, or iPhone 4(S) as examples of what I am looking for -- but with WP instead.

Thanks in advance for your suggestions.