I think you are being a little too concerned about the strength of a rotating band made of wood. If you use a hard wood it should be more than strong enough to hold the weight of the projectile. Turn it on a lathe, making careful calculations of the inside diameter, saw it in two, and glue it on with a good epoxy adhesive. The seam should be invisible after it is finished.
Using any sort of metal will cost you more than the value of the projectile, IMHO. Unless you already have the material in your scrap bucket.
You should be able to find photographs of originals to determine the dimensions and shape of an original band. If it’s a US Army or Navy projectile, there are all sorts of documents that have photos and/or drawings.
Here’s a photo of a 3"/23 Shrapnel cartridge in my collection. It had been fired so I replaced the rotating band with one that I made from copper. The steps I took were a little complicated and I would not have done it except that I had the copper on hand, and it was a garage project done more for pleasure than trying to save a few bucks.