You have said that your insurers will not pay for the alternative accommodation as your property is not a health hazard. Most insurance policies provide cover for "reasonable alternative accommodation costs if the insured property is uninhabitable". Being a health hazard and uninhabitable are not the same. It may pay you to check the exact wording of your policy and remind the insurers of this.
I have dealt with many insuance claims for fire and smoke/soot contamination and have only refused accommodation costs where the contamination is light. Insurers use specialist fire restoration companies and are usually guided by them. If, in their opinion, a property is uninhabitable then insurers should accept what they say - that is what they pay them for.
As far as a loss assessor is concerned, check what their fees are before signing anything if you go down this route. You could end up being out of pocket.
If a Loss Adjuster is involved, I would have a friendly chat to them and explain the position. It may be better to have them re-visit so you can point out your concerns. Most Loss Adjusters are quite friendly - well I am anyway.