No, not for needle poked fingers.
... Though keeping a band aid or two around is never amiss...
This time the paper tape is for thread. Thread, ribbon, embroidery floss, anything stringy and messy really.
The "gentle" paper tape is sticky enough to hold, but not too sticky, like some regular tape, so it's easy to remove and doesn't leave gross residue or badly pull on the fibers when you pull it off.
A little piece is great for keeping the thread from unraveling on spools that don't have a notch for holding the thread, like the green thread above. I use it also for the spools that do have the notch, like the brown thread. For me, it's just faster and more tidy than trying to catch the thread in the little slit or notch.
It's also great for embroidery floss, both like the blue above and the brown skein, below. Something I do, which works for me, with the skeins - which can be so messy! - is I pull off the tubular labels, save the one with the color number, cut it lengthwise and wrap it back around the floss. Then I secure the label back with a little piece of tape. You can use regular tape for this too, of course, since it's not touching the floss.
Another thing this tape is handy for is to use it in place of pins, when pins might get in the way, especially when using a sewing machine. Example: holding down a zipper or applique/trim to be stitched. Just be sure to test on an inconspicuous bit of fabric first, or on a scrap.
A tidy sewing room is a happy one! :)