I would agree in general the wrist HR monitors are not always as accurate as a chest strap. that being said, when I first started cycling it was the first time I used a chest strap with my garmin edge device for HR stats. about 2 years ago I decided i wanted to keep track of my HR for all my activities off the bike.
My son's old FitBit Blaze fits the bill perfect since it tracks HR, steps, sleep and can record certain activities like walk, run, bike, workouts which you sync to Fitbit app and then it syncs to my Strava. This older one requires the bluetooth connection to work via your phone first before it will record the GPS tracking.
the newest Fitbit devices look way better and I am deciding which one I want for my xmas gift because the only thing missing from this one for me is that its not waterproof (ask me how i know when I jumped in the pool with it on).
check out the latest Fitbit devices they have more features, sensors etc.. and i have found in general my HR compared to my garmin is pretty accurate when I ride the bike.