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...
Xperia Z C 6603; Stock LB, Root (101 F/W) (Son's)
Xperia Z C 6602; Stock LB, Root (101 F/W) (Wife's)
Moto E XT1022; Stock (Mine)
Nexus 7 (2012); EHNDROIX-V, Root (Son's)
Dell Venue 7 (2013); Stock 4.3, Root (Ours)
Asus TF 101; ARHD, Root (Mom's)
KitKat FAIL! Stick with Jellybean!