I know we don’t like to use chemicals, but many exterminators and products are known to be pet-safe, because they are chemicals that have no ill effects on them and dry almost immediately so a bunny never really ingests or inhales them. I have tried one kind with no bad effects on Sammy.
I am using the Ortho Home Defense Max spray bottle. What you can do it take the bunnies out of the room for play time elsewhere for an hour or so. Close their room and use a stream of this along the baseboard up against the wall, not in a wider spray, just right at the seams. Do the windows as well.
Let it dry and wait to bring bunnies back in. Also, when you spray, move anything of theirs, cage included, about a foot away from the wall so it doesn’t get hit. This stuff works with one use for months. I moved into an infested house, cleaned it up, sprayed this stuff generously, cleaned it more and moved in a week later. I have only seen a couple of dead ants since, and no live ones.
If you are still reluctant to do it in there, go outside your home and give a huge spray of this stuff all over the outside windows and ground of the walls. It is highly recommended for Outdoor use as well, and once they get it, they do not come back for weeks or months. What that may do, however, is send them inside your house just before they die off within the walls. But it’s the next best thing to spraying their room.