Firing any kind of a "projectile" is a bad idea for living history, whether its a lump of starch or a bullet, unless you are at a gun range.
National and State parks, for example, have very specific rules about this, and I've found its best to stick with them on any public setting.
However, more direct to your question, I have seen folks make historically accurate replica cartridges, string and all, for the purpose of blank firing living history loading demonstrations, but instead of any kind of ball or solid object, has perhaps a couple sheets of tissue paper stuffed in the head so the powder charge and all gives the exact size...
An original .58 minie cartridge...
The only negative with this, when blank firing, and perhaps ramming such a "stuffed" cartridge, is it adds to the burning paper fragments on firing considerably, so I can't recommend it.
Since I do most of my living history firing out of doors, and grass fires ruin the moment, I SHOW the public a cartridge like this (filled with sand), then replace it before going through the loading, and when going through the loading procedure, take out a simpler re-enactment type cartridge (no string, no tissue ball), tear and load...
To ram or not to ram the paper must be considered.
Some facilities allow for a simple living history firing demonstration loading the paper, and ramming, etc. But that would depend upon the rules of the site, park, museum, etc. Some don't mind demonstrating the rammer but don't want the paper down the barrel. I have also been to some that don't want us to either drop in the paper, or even use the rammer in blank demo. firing, so after charging cartridge there, we just go through the motions without drawing rammer, etc., and describe its use.
Consult the site on any rules on the subject, if any. Otherwise act with foremost discretion.
Of course it is not necessary to fire anything to demonstrate the loading methods of the period arms, and one can just go through the motions while describing them... Works pretty well, and you don't have to clean your gun.