A burnished or rounded leather cord sounds like a good idea. It would probably still have enough friction to keep it closed. fIt might also give it a more finished look.
I've used Preval cannisters for many things. If you just need a small amount of dye, you can clean them out to use for another small job later. For the most part, though, a full jar just about uses them up.
You're getting some nice, even dye jobs there. I like to use Fiebings or Lincoln dyes that can be thinned with alcohol. I then spray the piece with alcohol first so the dye takes more evenly. I also have never heard of using hot water. I've heard of people using plain water but not hot water. The whole idea is to slow down the dye from soaking in too fast and getting darker spots in the finish.
The exception to that is if I want to get a patchy finish, then I don't use alcohol first and dab it on with a cotton dauber getting it as textured as I want.
Cool. It's nice that the stamp is made from square stock. It will make it easier to line it up, assuming they made it aligned with one of the flat sides.
That one's only 2-3/4" across, just the right size. Besides, those blades don't getcha much once you get used to them. Getting used to them can be a challenge, though...