I use a bag I got from Bud Sports
https://buds-sports-us.com/
I got mine in 2021 the model was called the TravelBag. They do not seem to have one by that name anymore. But their RMTBAG ORIGINAL seems to be similar if not the same.
It's VERY well made and I highly recommend it.
A 63 is a very large bike. So, you'll have to do some checking with them on the fit. One of mine is a 60 and fits fine. I think a 63 would fit fine. The exception is, my saddle sticks up too high to fit inside. If you had to, you could lower your saddle for transport. In my case, I just let it stick up out of the bag. The bag can be zipped from both ends. Since I'm just tucking in behind my seats. it doesn't matter that the saddle sticks out.
You do remove both wheels. Though they have a model you only remove the front. For a road bike, you don't need to remove the bars. I bought the fork protector separately, but it looks like it is standard now. There is also an accessory for supporting the BB (Universal Bike Support). This keeps the weight off the chain rings. This mattered to me because I have the bike upright. It wouldn't matter if you were laying it on its side.
I got it so I could put it behind the front seats in my pickup for road trips. I could certainly fit the bike in by itself. But this was so much better because the wheels and everything were together. No worries about this or that rubbing on the bike frame. No worries about getting grease on something in the truck.
It's a soft bag with padding. Perfect for loading into your own vehicle. NO WAY I would check it on an airplane.
I made a point to "standardize" how I put the wheels in the pockets so the cassette was always against the same place. This made sure I didn't end up transferring grease or wax onto disc rotors.
I bought a separate chain/chain ring sleeve from Amazon. This prevents the chain from possibly slapping around and prevents getting grease or wax on the inside of the bag.
By the way, what is a "fixed hat deck"?