I don't like things which use apparatuses because they introduce a dependency (and since this scheme is for use in extreme/unusual circumstances, it's especially likely that Harry would not have leisure time or access to his pouch) and they make part of the process observable, hence, easier to realize the existence of & reverse-engineer.

A fully mental PRNG is doable under all circumstances in under a second and is unobservable except via Legilimency (which if it isn't blocked, means one is screwed anyway since one can just be False-memory-charmed into remembering having done the verification*).

* Kripkenstein would approve!