With respect to tradition the following plan has popped to mind.
First I'd need to get her mother's or sister's help getting the correct ring size. How does a guy have any chance of getting this info in secret? If I can get the proper sized ring give it to her father with a note, "mr X if I have earned the respect of you and your family I'd like to to pass this to your daughter, so that she can make her decition in discernment. Then at the time she feels ready either return it to me personally or via a serogate if her answer is no."
My immagination has also thought of one BAD outcome. So an alternate note might be, "I would like to ask you if I have earned your respect enough to ask for your daughter's hand. Remember my name isn't Jacob, I haven't been a shepherd for you for 7 years, and we are in the New Testiment time not the old!
Please pass this to your daughter with the instructions in discernment please decide if you or a serogate will return this to me."
Get's her family's approval and hers. Then Everyone gets to besurprised at some point. One last surprise for everyone is how I might respond and when after I get the ring back.