Maybe this will help http://www.howtoforge.com/using-ngx_pagespeed-with-nginx-on-debian-wheezy and http://www.howtoforge.com/using-ngx_pagespeed-with-nginx-on-debian-jessie-testing - right up your alley for Debian distro :)

I personally use CentOS build via Centmin Mod Nginx as it already includes ngx_pagespeed support out of the box http://centminmod.com/nginx_ngx_pagespeed.html :)

As to minimal downtime and risk, easiest would be to do a test run first, DigitalOcean VPS charged on an hourly basis is a good platform to do testing for end users wanting to make the jump from pre-packaged Nginx builds to source compilation. I suppose you could even automate the entire transition and shell script something to do all the leg work.