That should work, you might want to have some sort of structure to create a frame though, as chicken wire can be pretty floppy. I also have heard of baby bunnies fitting through 1 inch mesh, so you might want to go a mesh size down if your bun is small!
There’s some examples of housing made with chicken wire in this section: https://binkybunny.com/bunnyinfo/other-habitats/
They aren’t very temporary looking, but you might end up making something you like enough to just cancel your cage order!
You could also use dowels for supports, or even pieces of PVC (those would be easy to work with because they have joints for corners). They can cut PVC for you at the hardware store, or you buy a hand cutter to do it yourself.
Something like this would work (i don’t like the choice of fencing here because it’s plastic, but the frame looks good:

I like working with chicken wire because you can cut it and re-weave the ends together so it can be made very secure. Having some gloves and a pair of needle nose pliers helps a lot.
This was the product I got “Grayson Wood Residential Vinyl Sheet Flooring 12ft. Wide x Cut to Length”
It is slightly textured and my bunnies haven’t had any issues walking on it. They have you order the number of sq yards you want and enter that, but the roll is 12 ft wide (3 yards). So keep that in mind if you want one big piece with no seams. Like, if your area is 4 ft x 4 ft, you would want to order 4 sq yards so that you have one edge that’s 4 ft wide. You would have a bunch extra, but it’s pretty handy stuff to have around and it’s affordable.
.
.
.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.