how to disable birthday reminders in iOS and still view them in the calendar app?
Yes. This should work. As you are aware, when you (or the Facebook contact) inputs their birthday into the contact, iOS creates a new calendar called "Birthdays". On both iOS and OSX you have control over the notifications that you receive for each birthday that is on that calendar. 

Like you said you could can go and turn of the notifications which should prevent notifications from actually appearing. Note, however that the birthdays should still show in Notification Center.

You can also disable the Birthday calendar on your iOS device altogether by opening the Calendar.app, tapping "Calendars" in the upper left corner, and scrolling down to and tapping on "Birthdays". You will see the check mark next to it disappear and the birthdays will no longer show in your calendar. 

It, of course, would be easy to turn them back on temporarily in the future if you wanted to look up someone's birthday.