If it's really a matter of "polish" then the more reasonable approach would be to simply put up a warning while otherwise allowing full access to the application. If it's buggy, then it's buggy; oh well, at least we were warned.

If it's more a matter of some specific thing(s) that Chrome has implemented and other browsers haven't, then it'd be nice to be upfront about what that thing is so that those of us on non-Chrome browsers can bug e.g. Mozilla and Apple about it - and it would further be nice to actually test against the existence of that thing rather than gatekeeping the user agent string like it's 1999.