I've always deleted/disabled chrome and almost all google bundled bloatware on any phone/tablet in our house. I had a tough time shoehorning stock/aosp browser to replace chrome, till I stumbled onto lightning browser. Fast, lightweight, able to change search engine to DDG, able to change device string to whatever you want (Froyo N1) (just like AOSP), and works as a user app. I prefer downloading from their dedicated thread on XDA, or from the F-Droid store.
Dead Cookies leave no trails...