I would recommend letting the cats explore in the same room while the new bunny is still in its cage, and, of course, while you can be there to supervise.
I have a dwarf as well and a very, very playful cat. She thinks anything and everything is a toy and can get way too excited so we were very nervous to introduce them to each other. For the first month or so we would allow them in the same room, bun in her cage, and they seemed very curious about each other and were constantly sniffing each other. Once it came to the point where the cat was spending all of her time in the same room, sometimes even laying on top of the cage. This was about when we let the bun out so they could experience each other outside of the cage. She seemed to know to be gentle with Ashe, and seemed to instinctively know she wasn’t a toy. She did try to swat once or twice, but a nice playful swat which was much lighter than anything she would even greet us with, lol. I mean it still made us nervous, and we still don’t allow both out at the same time without supervision, but they love each other and get along great.
I would think that as long as you supervise at first they should be fine. Another thing we did was introduce them in a small space where the bun has a place to hide but the cat can’t reach. Make sure you can intervene if needed. Especially if your cats are more trained than mine, I don’t see there being any problems. Just go slow and make sure to judge when they’re ready to be introduced.
Another thing to consider may be the stress that’ll placed on the baby bun being introduced to both the other bun and the cats at the same time. If you can, provide the bunnies with their own space so the baby can get used to the new bun first, then the cats.
Good luck and sorry for the long reply lol

You cannot bond the baby rabbit with Wally until the new rabbit has been spayed or neutered, then a few weeks or a month has passed since their surgery.  I’m assuming that Wally is already neutered.  Wally and the new rabbit may get along at first, but as soon as the new bunny’s hormones come in, which can be around 12 weeks of age, everything will change, so it’s better to keep them separated from the beginning and wait the months until the new bunny can be spayed or neutered. They should be housed separately, and shouldn’t be allowed out to play and exercise together until after the surgery and recuperation and the wait for the hormones to abate. Then you can start the regular bonding procedures. When rabbits reach puberty, they can become aggressive. That can lead to fighting and severe injuries. There is also a chance, although it is a small chance, that any two rabbits will not get along and will never bond, and they will have to be kept separately their whole lives. Fortunately, that is rare, but it does happen. There are members here who were never able to bond their rabbits and they remain separate.