Advice on sewing bandages?
A couple options appear for your objective. Substitute sewing with fabric glue and apply sparsely. Most bandages of the sort you have pictured are elastic and would not take well to sewing, as you've noted. By the same token, they would also not take well to heavy adhesive application.

One would apply dots of adhesive spaced along the edges where overlapped, allowing the stretchy part to stretch, while keeping the glued portions small and spaced closely enough to avoid gaps but not so close as to eat up the stretch required for a good fit.

One would desire to keep the stretch forces to a minimum while applying the bandages on a suitable model arm and secure the bandages as needed with tape or similar products while the glue cures.

Testing would be desirable to determine how much stretch the glue can handle before failing, then adjust spacing accordingly.

Another option would be to use a carrier sleeve and glove, perhaps slightly oversized if such a factor is not a problem. The sleeve would reduce or prevent the stretching while either stitching or adhesive would secure the bandages in the desired locations. A suitable model would accelerate the process, as noted above. I don't believe it would be a simple matter to machine stitch on a sleeve and hand-stitching would require patience and determination.