I recommend you bite the bullet and trim the feathers on one of your arrows back to the quill. That is better than a bare shaft because it more closely replicates the spine of a fletched arrow since it has the weight of the quill and glue on the back of the arrow. I have a trimmed shaft for almost every arrow I've ever owned, and have used them countless times to test new bows or how changes in my form might affect tuning.
The problem with wrapping a fletched arrow is that the weight of the wrap will stiffen the spine of the arrow. Of course, trimming the feathers back to the quill weakens the spine of the arrow some, but not much, as the feathers that are trimmed off don't weigh much.
Leaving quills or a wrap on the back of the arrow does give the arrow some guidance, and it will begin to recover after 20 yards or so if it is close to being in tune, so the most accurate indication of bare shaft tuning with such arrows is at about 10 yards.