Ok, well I dont know what fire wool is but if it is ceramic fibre then it is not safe to have exposed in your living space!
The problem with this type of martial is after it has been heated, it is very likely to produce millions of air born microscopic particle into the living space, if it is disturbed or handled in any way.
These particles are not good as they can be absorbed into your body and possibly cause serious heath issues in later life.
If you use refractory wool or mat, then make sure it is sealed inside the stove and if you ever need to disturb it, wear a mask and hoover up everything afterwards, or use a damp cloth on any susceptible surfaces.
Fibergalss rope or titanium rope is much safer as the partials are larger however the dust from any refractory material should be treated with respect.
All refractory products sold in the EU will be reasonably safe before they are heated, they become especially hazardous when exposed to naked flame or high heat and then exposed to fresh air.
I would not worry to much in your case but, just be aware of potential issues.