I haven't checked on the latest software, but you should be able to go into Settings and still customise closed captions on either the NOW Stick or NOW Box.
To reach Settings, whilst on the home NOW screen on the Stick or Box press the back button on the remote (button next to home).
If the hidden left hand menu doesn't appear, then I noticed a glitch, where you need to click on the gear wheel icon and go into Cookies and click on the Accept All button.
Then go back to the NOW main screen and keep trying the back button until the hidden LHS menu appears (including Settiing).
Hopefully then under Settings > Captions you can change the subtitles appearance etc.