I have small purses, well tiny, that I keep my important items in, if they are not in the hotel in my suitcase or money belt. This is one of my favorites that can fit under my sweater/jacket or on top. I'm not going to lose it, and no one is getting into it unless I'm unconscious. The Pacsafe is my favorite for travel, but I also use this. I use these at home for my wallet so I don't have to carry a larger bag, but so I will always have my phone, keys and ID on me. Consequently, I am used to always having them attached to my body. I feel perfectly safe with my passport in my pacsafe particularly, and I would feel the same with the original Vaccine card.
However, I have a small item like this, that is for my days money and/or credit card and license, and if my Vaccine card worked alone or with my passport card, I'd feel comfortable with it in this small ID bag, that I would have attached to a ring on the inside of my purse (only due to the added Vax and PP card). I like to stick with a similar system to what I have at home, because I am really my worst problem, not others. Otherwise, this item is just zipped into a pocket or my purse. I often feel my money belt is redundant but will always travel with it, incase I feel better having everything attached to me in another manner. I'm one of the few who use a leg wallet for my money belt. Once on, I forget all about it until I crawl into bed and I see it is still on. Nonetheless, I am getting away from money belts it seems unless traveling solo.
Basically, there is no right or wrong, it is what ever works for you. I would only like that stashband if it made me look thin, and certainly not to be in and out of all day, but I wear black jeans so it would be inconvenient also.