Thanks for the confirmation.
1) Since the home is older, I recommend leaving the existing 3-way switches wired "as-is". Reason being is that on older homes, 3-way switches were wired much differently than we wire them today. Back in the day, electricians used a more complex wiring
method on 3-ways called either "California" or "Carter" switching methods. If disconnecting the existing wires, it may become a challenge in the future to get those 3-ways working properly again if the need ever arises. Even disconnecting the switches and making the proper wiring splices inside the wall box presents a challenge. Best to leave both switches "as-is". Not worth the aggravation in my opinion.
2) The fan can be wired directly to the ceiling box using the lone switched black and the lone white neutral wire. The fan remote will work fine, but one of the 3-way switches will always need to be turned ON in order for the remote to work.
Leave the other ceiling box wires spliced as is but remove the black tape and use wire nuts. Wire splices should have plastic wire nuts to securely splice wires together. Back in the day, splicing and taping wires was a common method, but also presents a potential safety issue without a wire nut.
3) If worried about accidentally turning OFF the switches, you can install 2 switch guard covers to prevent this. See link shown below for the switch guards sold at Home Depot.
Hope this helps………If you have any additional questions, let me know and I’ll be glad to answer them for you.
Otherwise, don’t forget to rate me before you log Off.
The next time you have an electrical question, you can also request for me at: http://www.justanswer.com/home-improvement/expert-your-electrician ……….Thanks…………..Kevin!