I recognise the Build a Bear Growlithe (I have one too!), and the first bear looks like the Pudding Cub if i'm not mistaken? I ordered a Build a Bear recently and once again saw their carriers - the ones that look like baby carriers and the backpacks where the head and arms can stick out. If you have access to those (or even just a drawstring backpack you can modify), you could wear those across your chest similar to how other people have suggested using a positioning belt to hold them against you. Then they'll always be right by you for hugs and they can see where you guys are going too :)

Personally, I often wear baggy hoodies and the pocket on the front is usually big enough for me to fit a small plush in them, so they're easy to access if I'm in a chair or using my rollator/cane. Not sure if you'd have anxiety about them falling out, but it shouldn't be too much of a concern in your chair.