Yeah, I use one of those. It’s pretty nice. The tag tape is available in aluminum and stainless steel; I use the latter. I use thin stainless wire to attach the labels with a technique that’s analogous to what @TheDerek described above, though with twin attachment points (both ends of the tape).
And as a matter of fact, I did receive it as a birthday present from my wife, so I can attest that your proposed acquisition technique works.
I did try a few of the aluminum tags this spring.
I also employ the plastic markers you stick in the soil.
And I’ve just about used up a roll of 500 of the adjustable plastic tags you place on the limbs or trunks.
In all cases, it’s frustrating to lose a tag (or let it fade until you can’t read it).