take Nexus 7 from android 4.3 to 4.2.2
I don't think the Nexus 7 (2013) ever had Android 4.2. I was going to suggest flashing a factory image but the only one available is Android 4.3 which suggests it's not possible.

As the other answers have suggested you will probably need to root to get the USB OTG functionality you are after.