Now that we know that our Sue has tried it, and it's *not* recommended, maybe you should see about padding the handlebars of your walker instead!
That might offer as much help as trying to "soften" the tires, and will be something you can control a bit easier.
One thing I have done with great success is to cut sections of pool noodles that are between 4 & 6 inches long (long enough to cover the original hand grips) and then I cut a slit down the length of each section. I slip each of the sections over the handlbars, and I use a length of my favorite stuff: the Velcro OneWrap! to wrap around and secure the pool noodle sections.
Here's a picture to show you what it looks like wrapped around the hand grip on my rollator:
View attachment 768320
It offers a good cushion for my hands and wrists, and doesn't interfere when I fold the walker. It won't make noisy wheels quieter, but it will help dampen vibrations that can make driving the walker uncomfortable. I can change them out easily whenever they lose their "squish"!