Can I pay with my phone if I switch to Cyanogenmod?
Yes flashing Cyanogenmod will enable you to pay using your banking app. Cyanogenmod does have support for the Open Mobile API.

 The Second approach however will be a bit tricky to do as I have not tried that. But I think its worth giving a try ! 
If it doesn't works, the first option will do just fine!.

PS : I like Cyanogenmod more than Oxygen OS, I suggest you that you use it as your daily driver.