As you said he wants to run application like website in browser. it sounds like that he just wants some sort of Shortcut for website. Then you just create an application and fire your event to run site URL in browser. as you said
all the fixes and updates are reflected in the application without having to re-install it.
means this is just a site. in other case use Phone gap (http://phonegap.com/) it matches your requirements and uses HTML for styling and almost all features of an typical site.
PhoneGap Support to Different Mobile Plateform (Claimed by PhoneGap)
http://docs.phonegap.com/en/edge/guide_support_index.md.html#Platform%20Support